<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><div class="t m0 x0 h1 y0 ff1 fs0 fc0 sc0 ls15 ws0">Solu¸<span class="_0 blank"></span><span class="ls16 ws1">c\u02dc<span class="_1 blank"></span><span class="ls17 ws2">oes dos Exerc<span class="_2 blank"></span>´<span class="_3 blank"></span><span class="ls18 ws3">\u0131cios da S<span class="_4 blank"> </span>e¸<span class="_0 blank"></span><span class="ls19 ws4">c\u02dc<span class="_5 blank"></span><span class="ls1a ws5">ao 4.1</span></span></span></span></span></div><div class="t m0 x1 h2 y1 ff1 fs1 fc0 sc0 ls1b ws6">1) <span class="ff2 ls1c ws7">A<span class="_6 blank"> </span>primeira<span class="_6 blank"> </span>p ergun<span class="_7 blank"></span>ta<span class="_6 blank"> </span>p o de<span class="_6 blank"> </span>ser<span class="_6 blank"> </span>resp ondida<span class="_6 blank"> </span>de<span class="_8 blank"> </span>5<span class="_6 blank"> </span>mo dos;<span class="_6 blank"> </span>a<span class="_6 blank"> </span>segunda,<span class="_6 blank"> </span>de<span class="_6 blank"> </span>5</span></div><div class="t m0 x0 h2 y2 ff2 fs1 fc0 sc0 ls1d ws8">mo dos,<span class="_6 blank"> </span>etc.</div><div class="t m0 x0 h2 y3 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e5<span class="_b blank"></span><span class="ff3 ls0">×<span class="ff2 ls1">5</span><span class="ls20 wsb">× ··· × <span class="ff2 ls2 wsc">5=5</span></span></span></span></div><div class="t m0 x2 h3 y4 ff4 fs2 fc0 sc0 ls21 wsd">10 <span class="ff2 fs1 ls22 wse v1">=9<span class="_c blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3 ws10">765</span>.<span class="ff2 ls3">625.</span></span></span></div><div class="t m0 x1 h2 y5 ff1 fs1 fc0 sc0 ls1b ws6">2) <span class="ff2 ls24 ws11">P<span class="_7 blank"></span>ara<span class="_d blank"> </span>formar<span class="_d blank"> </span>um<span class="_d blank"> </span>sub<span class="_4 blank"> </span>conjun<span class="_7 blank"></span>to, dev<span class="_7 blank"></span>e-se decidir, para<span class="_8 blank"> </span>cada elemen<span class="_7 blank"></span>to do</span></div><div class="t m0 x0 h2 y6 ff2 fs1 fc0 sc0 ls24 ws12">conjun<span class="_7 blank"></span>to,<span class="_e blank"> </span>se<span class="_f blank"> </span>ele<span class="_f blank"> </span>p ertencer´<span class="_10 blank"></span><span class="ls25 ws13">ao<span class="_11 blank"></span>un<span class="_11 blank"></span>\u02dc<span class="_12 blank"></span><span class="ls26 ws14">ao ao subconjunto.<span class="_13 blank"> </span>H´<span class="_10 blank"></span><span class="ls27 ws15">a2<span class="_7 blank"></span>m<span class="_11 blank"></span>o<span class="_14 blank"></span>d<span class="_11 blank"></span>o<span class="_11 blank"></span>sd<span class="_10 blank"></span>e</span></span></span></div><div class="t m0 x0 h2 y7 ff2 fs1 fc0 sc0 ls28 ws16">decidir o que fazer com o primeiro elemen<span class="_7 blank"></span>to do conjun<span class="_7 blank"></span>to, 2 mo<span class="_4 blank"> </span>dos com</div><div class="t m0 x0 h2 y8 ff2 fs1 fc0 sc0 ls29 ws17">o segundo, etc.</div><div class="t m0 x0 h2 y9 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e2<span class="_b blank"></span><span class="ff3 ls0">×<span class="ff2 ls1">2</span><span class="ls20 wsb">× ··· × <span class="ff2 ls2 wsc">2=2</span></span></span></span></div><div class="t m0 x2 h4 ya ff6 fs2 fc0 sc0 ls4">n<span class="ff2 fs1 ls23 v1">.</span></div><div class="t m0 x0 h2 yb ff1 fs1 fc0 sc0 ls2a ws18">Outra solu¸<span class="_10 blank"></span><span class="ls2b ws19">c\u02dc<span class="_15 blank"></span><span class="ls2c">ao:</span></span></div><div class="t m0 x0 h2 yc ff2 fs1 fc0 sc0 ls5 ws1a">Quando se acresce<span class="_7 blank"></span>n<span class="_7 blank"></span>ta um elemen<span class="_7 blank"></span>to a um conjun<span class="_7 blank"></span>to, os subconjuntos do</div><div class="t m0 x0 h2 yd ff2 fs1 fc0 sc0 ls2d ws1b">no<span class="_7 blank"></span>v<span class="_7 blank"></span>o conjun<span class="_7 blank"></span>to s\u02dc<span class="_10 blank"></span><span class="ls5 ws1c">ao<span class="_6 blank"> </span>os subconjun<span class="_7 blank"></span>tos do conjun<span class="_7 blank"></span>to original e<span class="_6 blank"> </span>estes unidos</span></div><div class="t m0 x0 h2 ye ff2 fs1 fc0 sc0 ls2e ws1d">ao no<span class="_7 blank"></span>v<span class="_7 blank"></span>o elemen<span class="_7 blank"></span>to.<span class="_16 blank"> </span>Ou seja, o n<span class="_4 blank"> </span>´<span class="_17 blank"></span><span class="ls2f ws1e">umero<span class="_8 blank"> </span>de<span class="_d blank"> </span>sub conjun<span class="_7 blank"></span>tos<span class="_8 blank"> </span>dobra.<span class="_16 blank"> </span>En<span class="_7 blank"></span>t\u02dc<span class="_17 blank"></span><span class="ls3">ao,</span></span></div><div class="t m0 x0 h2 yf ff2 fs1 fc0 sc0 ls30 ws1f">se <span class="ff5 ls23 wsf">A<span class="ff6 fs2 ls6 v2">n</span><span class="ff2 ws20 v0">´<span class="_10 blank"></span><span class="ls31 ws21">eon<span class="_9 blank"></span>´<span class="_18 blank"></span><span class="ls32 ws22">umero<span class="_d blank"> </span>de<span class="_8 blank"> </span>sub conjuntos<span class="_d blank"> </span>de<span class="_d blank"> </span>um<span class="_d blank"> </span>conjun<span class="_7 blank"></span>to<span class="_8 blank"> </span>com<span class="_d blank"> </span><span class="ff5 ls7">n</span><span class="ls2c ws23">elementos,</span></span></span></span></span></div><div class="t m0 x0 h5 y10 ff2 fs1 fc0 sc0 ls8">(<span class="ff5 ls23 wsf">A<span class="ff6 fs2 ls4 v2">n</span></span><span class="ls33 ws24 v0">)´<span class="_a blank"></span><span class="ls34 ws25">e uma progress\u02dc<span class="_17 blank"></span><span class="ls3 ws26">ao geom<span class="_7 blank"></span>´<span class="_10 blank"></span><span class="ls1c ws27">etrica de raz\u02dc<span class="_10 blank"></span><span class="ls9 ws28">ao<span class="_8 blank"> </span>2.<span class="_f blank"> </span>Logo, <span class="ff5 ls23 wsf">A<span class="ff6 fs2 lsa v2">n</span></span><span class="lsb">=<span class="ff5 ls23 wsf">A<span class="ff4 fs2 lsc v2">0</span>.</span><span class="lsd">2<span class="ff6 fs2 lsa v3">n</span><span class="ls35">=2</span></span></span></span></span></span></span></span></div><div class="t m0 x3 h4 y11 ff6 fs2 fc0 sc0 ls23">n</div><div class="t m0 x0 h2 y12 ff2 fs1 fc0 sc0 ls36 ws29">p<span class="_9 blank"></span>o<span class="_9 blank"></span>i<span class="_9 blank"></span>s<span class="_7 blank"></span>oc<span class="_9 blank"></span>o<span class="_19 blank"></span>n<span class="_19 blank"></span>j<span class="_9 blank"></span>u<span class="_19 blank"></span>n<span class="_19 blank"></span>t<span class="_9 blank"></span>ov<span class="_1a blank"></span>a<span class="_19 blank"></span>z<span class="_9 blank"></span>i<span class="_19 blank"></span>op<span class="_1b blank"></span>o<span class="_19 blank"></span>s<span class="_9 blank"></span>s<span class="_19 blank"></span>u<span class="_9 blank"></span>iu<span class="_9 blank"></span>m´<span class="_1c blank"></span><span class="ls23 ws2a">unico<span class="_6 blank"> </span>subconjunto.</span></div><div class="t m0 x1 h2 y13 ff1 fs1 fc0 sc0 ls1b ws6">3) <span class="ff2 ls28 ws2b">A primeira p<span class="_4 blank"> </span>essoa<span class="_1d blank"> </span>tem 5 escolhas;<span class="_1e blank"> </span>a s<span class="ls37 ws2c">egunda, 4; a terceira, 3.<span class="_d blank"> </span>A resposta</span></span></div><div class="t m0 x0 h2 y14 ff2 fs1 fc0 sc0 ls23 ws20">´<span class="_10 blank"></span><span class="ls38 ws2d">e5<span class="_b blank"></span><span class="ff3 ls0">×<span class="ff2 ls1">4</span>×<span class="ff2 ls3 ws2e">3 = 60.</span></span></span></div><div class="t m0 x1 h2 y15 ff1 fs1 fc0 sc0 ls1b ws2f">4) <span class="ff2 ls39 ws30">Os bancos em<span class="_1e blank"> </span>que os ho<span class="_4 blank"> </span>mens se sentam p<span class="_4 blank"> </span>o<span class="_1f blank"> </span>dem ser esco<span class="_4 blank"> </span>lhidos<span class="_1e blank"> </span>de 5<span class="_1f blank"> </span><span class="ff3 lse">×</span><span class="lsf">4<span class="ff3 ls23">×</span></span></span></div><div class="t m0 x0 h2 y16 ff2 fs1 fc0 sc0 lsf">3<span class="ff3 lse">×</span>2<span class="ff3 lse">×</span><span class="ls2c ws31">1<span class="_1e blank"> </span>=<span class="_1e blank"> </span>12 0<span class="_1d blank"> </span>mo dos,<span class="_1e blank"> </span>o<span class="_1d blank"> </span>mesmo<span class="_1e blank"> </span>o correndo<span class="_1d blank"> </span>com<span class="_1e blank"> </span>os<span class="_1d blank"> </span>bancos<span class="_1e blank"> </span>das<span class="_1d blank"> </span>m<span class="_7 blank"></span>ulheres.</span></div><div class="t m0 x0 h2 y17 ff2 fs1 fc0 sc0 ls24 ws12">Em<span class="_d blank"> </span>cada<span class="_d blank"> </span>banco,<span class="_f blank"> </span>os<span class="_d blank"> </span>casais<span class="_d blank"> </span>p o dem<span class="_d blank"> </span>se<span class="_d blank"> </span>s<span class="ls3a ws32">entar<span class="_d blank"> </span>de<span class="_d blank"> </span>2<span class="_20 blank"> </span>mo dos<span class="_d blank"> </span>diferentes.<span class="_21 blank"> </span>A</span></div><div class="t m0 x0 h6 y18 ff2 fs1 fc0 sc0 ls3b ws33">resp osta<span class="_1e blank"> </span>´<span class="_11 blank"></span><span class="ls3 ws34">e 120<span class="ff4 fs2 ls10 v3">2</span><span class="ff3 ls11 v0">×<span class="ff2 ls12">2<span class="ff4 fs2 ls13 v3">5</span><span class="ls3 ws35">= 460<span class="ff5 ls23 wsf">.</span>800.</span></span></span></span></div><div class="t m0 x1 h2 y19 ff1 fs1 fc0 sc0 ls1b ws6">5) <span class="ff2 ls3c ws36">As 64 casas do tabuleiro dividem-se,<span class="_8 blank"> </span>naturalmente, em tr<span class="_7 blank"></span>\u02c6<span class="_10 blank"></span><span class="ls14 ws37">es<span class="_8 blank"> </span>grup os:</span></span></div><div class="t m0 x0 h2 y1a ff2 fs1 fc0 sc0 ls3d ws38">i) as 4 casas dos v<span class="_7 blank"></span>´<span class="_17 blank"></span><span class="ls3e">ertices;</span></div><div class="t m0 x0 h2 y1b ff2 fs1 fc0 sc0 ls5 ws39">ii) as 24 casas da b<span class="_4 blank"> </span>orda do<span class="_8 blank"> </span>tabuleiro, mas que n\u02dc<span class="_3 blank"></span><span class="ls3 ws3a">ao s\u02dc<span class="_17 blank"></span>ao<span class="_8 blank"> </span>v<span class="_7 blank"></span>´<span class="_10 blank"></span><span class="ls3e">ertices;</span></span></div><div class="t m0 x0 h2 y1c ff2 fs1 fc0 sc0 ls3f ws38">iii) as restan<span class="_7 blank"></span>tes 36 casas,<span class="_8 blank"> </span>que<span class="_8 blank"> </span>s\u02dc<span class="_17 blank"></span><span class="ls40 ws3b">ao in<span class="_7 blank"></span>teriores ao tabuleiro.</span></div><div class="t m0 x0 h2 y1d ff2 fs1 fc0 sc0 ls8 ws3c">V<span class="_b blank"></span>amos separar a nossa c<span class="_7 blank"></span>on<span class="_7 blank"></span>tagem conforme o tipo de casa o<span class="_4 blank"> </span>cupada p<span class="_4 blank"> </span>elo</div><div class="t m0 x0 h2 y1e ff2 fs1 fc0 sc0 ls40 ws3d">rei negro:</div><div class="t m0 x0 h2 y1f ff2 fs1 fc0 sc0 ls2d ws3e">i) h´<span class="_17 blank"></span><span class="ls3f ws3f">a<span class="_8 blank"> </span>4 p<span class="_4 blank"> </span>ossibilidades<span class="_8 blank"> </span>para o rei negro<span class="_8 blank"> </span>e 60 para o rei branco;</span></div><div class="t m0 x0 h2 y20 ff2 fs1 fc0 sc0 ls41 ws40">ii) h´<span class="_17 blank"></span><span class="ls29 ws17">a<span class="_8 blank"> </span>24 p<span class="_4 blank"> </span>ossibilidades<span class="_8 blank"> </span>para o rei negro<span class="_8 blank"> </span>e 58 para o rei branco;</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><div class="t m0 x0 h2 y0 ff2 fs1 fc0 sc0 ls3c ws42">iii) h´<span class="_17 blank"></span><span class="ls29 ws17">a<span class="_8 blank"> </span>36 p<span class="_4 blank"> </span>ossibilidades<span class="_8 blank"> </span>para o rei negro<span class="_8 blank"> </span>e 55 para o rei branco.</span></div><div class="t m0 x0 h2 y21 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e4<span class="_b blank"></span><span class="ff3 ls0">×<span class="ff2 ls3 ws43">60 +<span class="_1d blank"> </span>24 </span>×<span class="ff2 ls3 ws43">58 + 36 </span>×<span class="ff2 ls3 ws2e">55 = 3612.</span></span></span></div><div class="t m0 x0 h2 y22 ff2 fs1 fc0 sc0 ls41 ws44">Se os reis<span class="_d blank"> </span>s\u02dc<span class="_17 blank"></span><span class="ls4e ws45">a<span class="_4 blank"> </span>o iguais,<span class="_d blank"> </span>a resp<span class="_1f blank"> </span>osta passa<span class="_20 blank"> </span>a ser a metade<span class="_d blank"> </span>da r<span class="_4 blank"> </span>esp<span class="_4 blank"> </span>osta<span class="_d blank"> </span>an-</span></div><div class="t m0 x0 h2 y23 ff2 fs1 fc0 sc0 ls4f ws46">terior,<span class="_6 blank"> </span>p ois,<span class="_6 blank"> </span>tro cando<span class="_6 blank"> </span>a<span class="_6 blank"> </span>posi¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls34 ws48">ao dos reis, agora obt´<span class="_10 blank"></span><span class="ls51 ws49">em-se<span class="_8 blank"> </span>a mesma con<span class="_4 blank"> </span>-</span></span></span></div><div class="t m0 x0 h2 y24 ff2 fs1 fc0 sc0 ls14 ws4a">\ufb01gura¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_17 blank"></span><span class="ls3">ao.</span></span></div><div class="t m0 x1 h2 y25 ff1 fs1 fc0 sc0 ls1b ws6">6) <span class="ff2 ws4b">Ha<span class="_7 blank"></span>v<span class="_7 blank"></span>er´<span class="_17 blank"></span><span class="ls29 ws4c">a uma torre em cada linha e em cada coluna.<span class="_f blank"> </span>A p<span class="_4 blank"> </span>osi¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls14 ws4d">ao da torre</span></span></span></span></div><div class="t m0 x0 h2 y26 ff2 fs1 fc0 sc0 ls52 ws4e">da primeira linha<span class="_d blank"> </span>p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>de<span class="_d blank"> </span>ser escolhida<span class="_d blank"> </span>de 8 mo<span class="_4 blank"> </span>dos;<span class="_d blank"> </span>a<span class="_d blank"> </span>da segunda<span class="_d blank"> </span>linha,</div><div class="t m0 x0 h2 y27 ff2 fs1 fc0 sc0 ls2e ws4f">de 7, etc.</div><div class="t m0 x0 h2 y28 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e8<span class="_b blank"></span><span class="ff3 ls0">×<span class="ff2 ls1">7</span><span class="ls11">×<span class="ff2 ls1">6</span></span>×<span class="ff2 ls1">5</span><span class="ls11">×<span class="ff2 ls1">4</span></span>×<span class="ff2 ls1">3</span>×<span class="ff2 ls42">2</span>×<span class="ff2 ls2 wsc">1=4<span class="_1b blank"></span>0<span class="_1b blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3">320.</span></span></span></span></span></div><div class="t m0 x0 h2 y29 ff2 fs1 fc0 sc0 ls3a ws50">Se as torres fossem<span class="_8 blank"> </span>diferentes, para<span class="_8 blank"> </span>cada uma da<span class="_4 blank"> </span>s escolhas de<span class="_8 blank"> </span>p<span class="_4 blank"> </span>osi¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls3">ao,</span></span></div><div class="t m0 x0 h2 y2a ff2 fs1 fc0 sc0 ls2d ws51">ter<span class="_b blank"></span>´<span class="_1a blank"></span><span class="ls53 ws52">\u0131amos<span class="_6 blank"> </span>que<span class="_8 blank"> </span>escolher<span class="_8 blank"> </span>uma<span class="_6 blank"> </span>das<span class="_8 blank"> </span>torres.<span class="_f blank"> </span>A<span class="_6 blank"> </span>resp o sta<span class="_6 blank"> </span>seria,<span class="_6 blank"> </span>p o rtan<span class="_7 blank"></span>to,</span></div><div class="t m0 x0 h2 y2b ff2 fs1 fc0 sc0 ls42">8<span class="ff3 ls11">×</span>8<span class="ff3 ls43">×</span>7<span class="ff3 ls11">×</span>7<span class="ff3 ls11">×</span>6<span class="ff3 ls11">×</span>6<span class="ff3 ls11">×</span>5<span class="ff3 ls11">×</span>5<span class="ff3 ls11">×</span>4<span class="ff3 ls54 ws53">××<span class="_22 blank"></span><span class="ff2 ls42">3<span class="ff3 ls54">××<span class="_22 blank"></span><span class="ff2 ls42">3<span class="ff3 ls11">×</span>2<span class="ff3 ls11">×</span>2<span class="ff3 ls11">×</span>1<span class="ff3 ls11">×</span><span class="ls55 ws54">1=(<span class="_c blank"></span>8<span class="_c blank"></span>!<span class="_c blank"></span>)</span></span></span></span></span></div><div class="t m0 x4 h3 y2c ff4 fs2 fc0 sc0 ls13">2<span class="ff2 fs1 ls23 v1">=</span></div><div class="t m0 x0 h2 y2d ff2 fs1 fc0 sc0 ls44">1<span class="ff5 ls23 wsf">.</span><span class="ls3 ws10">625</span><span class="ff5 ls23 wsf">.</span><span class="ls3 ws10">702</span><span class="ff5 ls23 wsf">.</span><span class="ls3">400.</span></div><div class="t m0 x1 h2 y2e ff1 fs1 fc0 sc0 ls1b ws6">7) <span class="ff2 ls2f ws55">Se a primeira carta<span class="_1d blank"> </span>´<span class="_10 blank"></span><span class="ls1c ws56">e o rei de<span class="_6 blank"> </span>c<span class="_7 blank"></span>opas, a<span class="_6 blank"> </span>segunda po<span class="_1f blank"> </span>de ser escolhida<span class="_6 blank"> </span>de 48</span></span></div><div class="t m0 x0 h2 y2f ff2 fs1 fc0 sc0 ls56 ws57">mo dos<span class="_1d blank"> </span>(p o de<span class="_1e blank"> </span>ser<span class="_1e blank"> </span>qualquer<span class="_1d blank"> </span>carta,<span class="_1e blank"> </span>exceto<span class="_1e blank"> </span>o s<span class="_1d blank"> </span>4<span class="_1e blank"> </span>reis).<span class="_20 blank"> </span>Se<span class="_1e blank"> </span>a<span class="_1e blank"> </span>primeira<span class="_1e blank"> </span>carta<span class="_1d blank"> </span>´<span class="_10 blank"></span><span class="ls23">e</span></div><div class="t m0 x0 h2 y30 ff2 fs1 fc0 sc0 ls1b ws58">de copas mas n\u02dc<span class="_17 blank"></span><span class="ls3 ws59">ao ´<span class="_11 blank"></span><span class="ls57 ws5a">e<span class="_23 blank"> </span>o<span class="_23 blank"> </span>rei,<span class="_1d blank"> </span>ela<span class="_1d blank"> </span>p o de<span class="_23 blank"> </span>ser<span class="_23 blank"> </span>esco lhida<span class="_23 blank"> </span>de<span class="_1d blank"> </span>12<span class="_23 blank"> </span>mo dos.<span class="_20 blank"> </span>Neste<span class="_1d blank"> </span>caso,</span></span></div><div class="t m0 x0 h2 y31 ff2 fs1 fc0 sc0 ls3c ws5b">a<span class="_23 blank"> </span>segunda<span class="_1d blank"> </span>carta<span class="_23 blank"> </span>p o de<span class="_23 blank"> </span>ser<span class="_1d blank"> </span>escolhida<span class="_23 blank"> </span>de<span class="_1d blank"> </span>47<span class="_23 blank"> </span>mo dos<span class="_23 blank"> </span>(n\u02dc<span class="_10 blank"></span>ao<span class="_1d blank"> </span>po de<span class="_1d blank"> </span>ser<span class="_23 blank"> </span>a<span class="_23 blank"> </span>primeira</div><div class="t m0 x0 h2 y32 ff2 fs1 fc0 sc0 ls2e ws5c">escolhida,<span class="_8 blank"> </span>nem<span class="_6 blank"> </span>nenhum<span class="_6 blank"> </span>dos<span class="_6 blank"> </span>4<span class="_6 blank"> </span>r eis).<span class="_f blank"> </span>A<span class="_6 blank"> </span>resp osta<span class="_6 blank"> </span>´<span class="_11 blank"></span><span class="ls1f wsa">e4<span class="_9 blank"></span>8<span class="_b blank"></span>+<span class="_b blank"></span>1<span class="_9 blank"></span>2<span class="_b blank"></span><span class="ff3 ls11">×<span class="ff2 ls3 ws5d">47 = 612.</span></span></span></div><div class="t m0 x1 h2 y33 ff1 fs1 fc0 sc0 ls1b ws6">8) <span class="ff2 ls24 ws5e">a) P<span class="_7 blank"></span>ara construir uma fun¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls2e ws5f">ao,<span class="_d blank"> </span>dev<span class="_7 blank"></span>emos, pa<span class="_4 blank"> </span>ra cada elemento de<span class="_8 blank"> </span>A, es-</span></span></span></div><div class="t m0 x0 h2 y34 ff2 fs1 fc0 sc0 ls1d ws60">colher sua imagem em B. H´<span class="_10 blank"></span><span class="ls58 ws61">a7m<span class="_c blank"></span>o<span class="_22 blank"></span>d<span class="_22 blank"></span>o<span class="_c blank"></span>sd<span class="_c blank"></span>ee<span class="_24 blank"></span>s<span class="_c blank"></span>c<span class="_24 blank"></span>o<span class="_c blank"></span>l<span class="_24 blank"></span>h<span class="_24 blank"></span>e<span class="_c blank"></span>r ai<span class="_24 blank"></span>m<span class="_24 blank"></span>a<span class="_c blank"></span>g<span class="_24 blank"></span>e<span class="_24 blank"></span>md<span class="_c blank"></span>op<span class="_24 blank"></span>r<span class="_24 blank"></span>i<span class="_c blank"></span>m<span class="_24 blank"></span>e<span class="_c blank"></span>i<span class="_24 blank"></span>r<span class="_24 blank"></span>o</span></div><div class="t m0 x0 h2 y35 ff2 fs1 fc0 sc0 ls52 ws62">elemen<span class="_7 blank"></span>to de<span class="_20 blank"> </span>A, 7 mo<span class="_1f blank"> </span>dos de escolher<span class="_20 blank"> </span>a imagem do segundo<span class="_f blank"> </span>elemen<span class="_7 blank"></span>to,</div><div class="t m0 x0 h2 y36 ff2 fs1 fc0 sc0 ls57">etc.</div><div class="t m0 x0 h2 y37 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e7<span class="_b blank"></span><span class="ff3 ls0">×<span class="ff2 ls1">7</span><span class="ls11">×<span class="ff2 ls1">7</span></span>×<span class="ff2 ls55 ws54">7=2<span class="_c blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3">401.</span></span></span></span></span></div><div class="t m0 x0 h2 y38 ff2 fs1 fc0 sc0 ls3c ws63">b) P<span class="_7 blank"></span>ara a fun¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls3a ws64">ao ser inj<span class="_4 blank"> </span>etora, elementos diferen<span class="_7 blank"></span>tes dev<span class="_7 blank"></span>em ter ima<span class="_4 blank"> </span>gens</span></span></div><div class="t m0 x0 h2 y39 ff2 fs1 fc0 sc0 ls53 ws65">diferen<span class="_7 blank"></span>tes. H´<span class="_17 blank"></span><span class="ls59 ws66">a7m<span class="_9 blank"></span>o<span class="_1b blank"></span>d<span class="_9 blank"></span>o<span class="_9 blank"></span>sd<span class="_9 blank"></span>ee<span class="_19 blank"></span>s<span class="_9 blank"></span>c<span class="_9 blank"></span>o<span class="_9 blank"></span>l<span class="_9 blank"></span>h<span class="_19 blank"></span>e<span class="_9 blank"></span>r ai<span class="_9 blank"></span>m<span class="_9 blank"></span>a<span class="_9 blank"></span>g<span class="_19 blank"></span>e<span class="_9 blank"></span>md<span class="_9 blank"></span>op<span class="_9 blank"></span>r<span class="_9 blank"></span>i<span class="_19 blank"></span>m<span class="_9 blank"></span>e<span class="_9 blank"></span>i<span class="_9 blank"></span>r<span class="_9 blank"></span>oe<span class="_9 blank"></span>l<span class="_19 blank"></span>e<span class="_9 blank"></span>m<span class="_9 blank"></span>e<span class="_9 blank"></span>n<span class="_19 blank"></span>t<span class="_19 blank"></span>o d<span class="_9 blank"></span>e</span></div><div class="t m0 x0 h2 y3a ff2 fs1 fc0 sc0 ls2d ws67">A, 6 mo<span class="_4 blank"> </span>dos de<span class="_8 blank"> </span>escolher a imagem<span class="_8 blank"> </span>do segundo elemento, etc.</div><div class="t m0 x0 h2 y3b ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e7<span class="_b blank"></span><span class="ff3 ls0">×<span class="ff2 ls1">6</span><span class="ls11">×<span class="ff2 ls1">5</span></span>×<span class="ff2 ls3 ws2e">4 = 840.</span></span></span></div><div class="t m0 x1 h7 y3c ff1 fs1 fc0 sc0 ls1b ws6">9) <span class="ff2 ls3 ws68">a)<span class="_6 blank"> </span>Como<span class="_6 blank"> </span>720 = 2<span class="ff4 fs2 ls45 v3">4</span><span class="ff3 ls46 v0">×<span class="ff2 ls47">3<span class="ff4 fs2 ls45 v3">2</span></span><span class="ls0">×<span class="ff2 ls48">5<span class="ff4 fs2 ls49 v3">1</span><span class="ls3 ws69">,<span class="_8 blank"> </span>720<span class="_6 blank"> </span>p ossui<span class="_6 blank"> </span>5<span class="_1d blank"> </span></span></span></span>×<span class="ff2 ls1">3</span>×<span class="ff2 ls5a ws6a">2 = 30<span class="_8 blank"> </span>divisores.<span class="_e blank"> </span>Ao<span class="_4 blank"> </span>s</span></span></span></div><div class="t m0 x0 h2 y3d ff2 fs1 fc0 sc0 ls14 ws6b">pares, estes d<span class="_7 blank"></span>ivisores formam<span class="_1d blank"> </span>produtos iguais a<span class="_1d blank"> </span>720.<span class="_d blank"> </span>Logo, h´<span class="_17 blank"></span><span class="ls5b ws6c">a1<span class="_24 blank"></span>5m<span class="_c blank"></span>o<span class="_22 blank"></span>d<span class="_24 blank"></span>o<span class="_24 blank"></span>s</span></div><div class="t m0 x0 h2 y3e ff2 fs1 fc0 sc0 ls2c ws26">de escrev<span class="_7 blank"></span>er<span class="_8 blank"> </span>720 como um<span class="_8 blank"> </span>pro<span class="_4 blank"> </span>duto<span class="_8 blank"> </span>de divisores.</div><div class="t m0 x0 h8 y3f ff2 fs1 fc0 sc0 ls14 ws6d">b) Como 144<span class="_f blank"> </span>=<span class="_f blank"> </span>2<span class="ff4 fs2 ls4a v3">4</span><span class="ff3 ls4b v0">×<span class="ff2 ls4c">3<span class="ff4 fs2 lsc v3">2</span><span class="ls3 ws69">,<span class="_e blank"> </span>144<span class="_20 blank"> </span>p ossui<span class="_f blank"> </span>3<span class="_1e blank"> </span></span></span><span class="ls4d">×<span class="ff2 ls4e ws6e">3 =<span class="_e blank"> </span>9 divisores.<span class="_13 blank"> </span>Com eles,</span></span></span></div><div class="t m0 x0 h2 y40 ff2 fs1 fc0 sc0 ls24 ws6f">p o dem<span class="_d blank"> </span>ser<span class="_f blank"> </span>formados<span class="_d blank"> </span>4<span class="_20 blank"> </span>pares<span class="_f blank"> </span>de<span class="_20 blank"> </span>divisores<span class="_20 blank"> </span>cujo<span class="_20 blank"> </span>pro duto<span class="_d blank"> </span>´<span class="_11 blank"></span><span class="ls3 ws70">e 144 e,<span class="_20 blank"> </span>al´<span class="_17 blank"></span><span class="ls50">em</span></span></div><div class="t m0 x5 h2 y41 ff2 fs1 fc0 sc0 ls23">2</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><div class="t m0 x0 h2 y0 ff2 fs1 fc0 sc0 ls29 ws71">disso,<span class="_e blank"> </span>p<span class="_4 blank"> </span>o<span class="_1f blank"> </span>de ser formado o pro<span class="_4 blank"> </span>duto 12<span class="_6 blank"> </span><span class="ff3 ls5c">×</span><span class="ls5 ws72">12.<span class="_13 blank"> </span>Assim, h´<span class="_17 blank"></span><span class="ls27 ws15">a5m<span class="_11 blank"></span>o<span class="_14 blank"></span>d<span class="_11 blank"></span>o<span class="_11 blank"></span>sd<span class="_11 blank"></span>e</span></span></div><div class="t m0 x0 h2 y42 ff2 fs1 fc0 sc0 ls2c ws26">escrev<span class="_7 blank"></span>er<span class="_8 blank"> </span>144 como um pro<span class="_1f blank"> </span>duto de diviso<span class="_4 blank"> </span>res.</div><div class="t m0 x6 h2 y22 ff1 fs1 fc0 sc0 ls1b ws73">10) <span class="ff2 ls24 ws74">Um arm´<span class="_17 blank"></span><span class="ls23 ws75">ario \ufb01car´<span class="_10 blank"></span><span class="ls52 ws76">a<span class="_1e blank"> </span>ab erto<span class="_1e blank"> </span>se<span class="_6 blank"> </span>ele<span class="_1e blank"> </span>for<span class="_1e blank"> </span>mexido<span class="_25 blank"> </span>um<span class="_1e blank"> </span>n ´<span class="_3 blank"></span><span class="ls53 ws77">umero ´<span class="_19 blank"></span><span class="ls70 ws75">\u0131mpar de v<span class="_7 blank"></span>ezes.</span></span></span></span></span></div><div class="t m0 x0 h2 y23 ff2 fs1 fc0 sc0 ls4f ws78">P<span class="_7 blank"></span>or outro lado,<span class="_e blank"> </span>o arm´<span class="_3 blank"></span><span class="ls1b ws79">ario<span class="_f blank"> </span>de<span class="_e blank"> </span>ordem <span class="ff5 ls5d">k</span><span class="ls23 ws20">´<span class="_10 blank"></span><span class="ls5a ws7a">e<span class="_f blank"> </span>mexido<span class="_e blank"> </span>p elas<span class="_f blank"> </span>p essoas<span class="_f blank"> </span>cuj os</span></span></span></div><div class="t m0 x0 h2 y24 ff2 fs1 fc0 sc0 ls71 ws7b">n´<span class="_15 blank"></span><span class="ls1c ws7c">umeros s\u02dc<span class="_10 blank"></span><span class="ls3b ws7d">ao divisores de <span class="ff5 ls5e">k</span><span class="ls72 ws7e">.<span class="_26 blank"> </span>Logo, estar\u02dc<span class="_3 blank"></span><span class="ls5f ws7f">ao ab<span class="_4 blank"> </span>ertos os arm´<span class="_10 blank"></span><span class="ls60 ws80">arios cujos</span></span></span></span></span></div><div class="t m0 x0 h2 y43 ff2 fs1 fc0 sc0 ls71 ws7b">n´<span class="_15 blank"></span><span class="ls21 ws81">umero s<span class="_8 blank"> </span>p ossuem<span class="_20 blank"> </span>um<span class="_d blank"> </span>n ´<span class="_3 blank"></span><span class="ls53 ws82">umero ´<span class="_19 blank"></span><span class="ls37 ws83">\u0131mpar<span class="_d blank"> </span>de<span class="_d blank"> </span>divisores.<span class="_27 blank"> </span>Isto<span class="_d blank"> </span>o corre<span class="_d blank"> </span>com<span class="_8 blank"> </span>os</span></span></span></div><div class="t m0 x0 h2 y44 ff2 fs1 fc0 sc0 ls71 ws7b">n´<span class="_15 blank"></span><span class="ls4e ws83">umero s<span class="_6 blank"> </span>cuj os<span class="_8 blank"> </span>exp o entes<span class="_8 blank"> </span>s\u02dc<span class="_10 blank"></span><span class="ls8 ws84">ao<span class="_8 blank"> </span>to<span class="_1f blank"> </span>dos<span class="_6 blank"> </span>pares<span class="_8 blank"> </span>na<span class="_d blank"> </span>decomposi¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_17 blank"></span><span class="ls61 ws85">ao<span class="_d blank"> </span>em fatores</span></span></span></span></div><div class="t m0 x0 h2 y45 ff2 fs1 fc0 sc0 ls5f ws86">primos, ou<span class="_d blank"> </span>seja, s<span class="_7 blank"></span>\u02dc<span class="_17 blank"></span><span class="ls53 ws52">ao<span class="_20 blank"> </span>quadrados<span class="_20 blank"> </span>p erfeitos.<span class="_21 blank"> </span>Assim,<span class="_20 blank"> </span>p ermanecer\u02dc<span class="_17 blank"></span><span class="ls3 ws69">ao<span class="_20 blank"> </span>ab er-</span></span></div><div class="t m0 x0 h2 y46 ff2 fs1 fc0 sc0 ls61 ws87">tos os arm´<span class="_10 blank"></span><span class="ls60 ws88">arios<span class="_8 blank"> </span>cujos<span class="_8 blank"> </span>n ´<span class="_17 blank"></span><span class="ls1c ws89">umeros s\u02dc<span class="_17 blank"></span><span class="ls60 ws8a">ao quadrados perfeitos, ou s<span class="_7 blank"></span>eja, os<span class="_8 blank"> </span>de</span></span></span></div><div class="t m0 x0 h9 y47 ff2 fs1 fc0 sc0 ls71 ws7b">n´<span class="_15 blank"></span><span class="ls2f ws8b">umeros 1<span class="ff4 fs2 lsc v3">2</span><span class="ff5 ls62 v0">,<span class="ff2 ls63">2<span class="ff4 fs2 ls49 v3">2</span></span><span class="ls64 ws8c">,...,<span class="ff2 ls3 ws10">30<span class="ff4 fs2 ls49 v3">2</span><span class="ls23">.</span></span></span></span></span></div><div class="t m0 x6 h2 y48 ff1 fs1 fc0 sc0 ls1b ws73">11) <span class="ff2 ls37 ws8d">Separemos o caso em que o primeiro e o terceiro quadran<span class="_7 blank"></span>tes t<span class="_7 blank"></span>\u02c6<span class="_10 blank"></span><span class="ls70 ws8e">em cores</span></span></div><div class="t m0 x0 h2 y49 ff2 fs1 fc0 sc0 ls2a ws8f">iguais do caso em que eles t\u02c6<span class="_10 blank"></span><span class="ls57 ws90">em<span class="_8 blank"> </span>cores diferentes.</span></div><div class="t m0 x0 h2 y4a ff2 fs1 fc0 sc0 ls1d ws91">No caso de cores ig<span class="_4 blank"> </span>uais,<span class="_e blank"> </span>h´<span class="_17 blank"></span>a 5 mo<span class="_1f blank"> </span>dos de escolher<span class="_e blank"> </span>a cor<span class="_e blank"> </span>´<span class="_3 blank"></span><span class="ls37 ws92">unica para o</span></div><div class="t m0 x0 h2 y4b ff2 fs1 fc0 sc0 ls24 ws93">primeiro e o terceiro quadran<span class="_7 blank"></span>tes,<span class="_28 blank"> </span>4 mo<span class="_4 blank"> </span>dos de escolher a cor para o</div><div class="t m0 x0 h2 y4c ff2 fs1 fc0 sc0 ls24 ws94">segundo quadran<span class="_7 blank"></span>te<span class="_1d blank"> </span>e 4 mo<span class="_4 blank"> </span>dos de<span class="_1d blank"> </span>escolher a cor<span class="_1d blank"> </span>para o quarto quadran<span class="_7 blank"></span>te.</div><div class="t m0 x0 h2 y4d ff2 fs1 fc0 sc0 ls3c ws95">H´<span class="_17 blank"></span><span class="ls44 ws96">a,<span class="_20 blank"> </span>p ortan<span class="_7 blank"></span>to,<span class="_20 blank"> </span>5<span class="_1d blank"> </span><span class="ff3 ls65">×</span><span class="ls66">4<span class="ff3 ls65">×</span><span class="ls61 ws70">4 = 80 mo<span class="_4 blank"> </span>dos de colorir o mapa usando cores</span></span></span></div><div class="t m0 x0 h2 y4e ff2 fs1 fc0 sc0 ls2d ws97">iguais no primeiro e no terceiro quadran<span class="_7 blank"></span>tes.</div><div class="t m0 x0 h2 y4f ff2 fs1 fc0 sc0 ls57 ws98">No caso<span class="_1d blank"> </span>de cores<span class="_1d blank"> </span>diferen<span class="_7 blank"></span>tes,<span class="_1d blank"> </span>h´<span class="_10 blank"></span><span class="ls73 ws99">a5m<span class="_22 blank"></span>o<span class="_29 blank"></span>d<span class="_22 blank"></span>o<span class="_22 blank"></span>sd<span class="_22 blank"></span>ee<span class="_24 blank"></span>s<span class="_22 blank"></span>c<span class="_22 blank"></span>o<span class="_22 blank"></span>l<span class="_22 blank"></span>h<span class="_22 blank"></span>e<span class="_22 blank"></span>rac<span class="_22 blank"></span>o<span class="_22 blank"></span>rp<span class="_22 blank"></span>a<span class="_22 blank"></span>r<span class="_22 blank"></span>aop<span class="_22 blank"></span>r<span class="_22 blank"></span>i<span class="_22 blank"></span>m<span class="_24 blank"></span>e<span class="_22 blank"></span>i<span class="_22 blank"></span>r<span class="_22 blank"></span>o</span></div><div class="t m0 x0 h2 y50 ff2 fs1 fc0 sc0 ls28 ws9a">quadran<span class="_7 blank"></span>te,<span class="_1d blank"> </span>4 mo<span class="_1f blank"> </span>dos de escolher<span class="_1d blank"> </span>a cor<span class="_1d blank"> </span>para o terceiro<span class="_1d blank"> </span>quadran<span class="_7 blank"></span>te,<span class="_1d blank"> </span>3 mo<span class="_4 blank"> </span>do<span class="_4 blank"> </span>s</div><div class="t m0 x0 h2 y51 ff2 fs1 fc0 sc0 ls3f ws9b">de escolher a cor para o segundo quadrante e 3 modos de escolher<span class="_25 blank"> </span>a cor</div><div class="t m0 x0 h2 y52 ff2 fs1 fc0 sc0 ls40 ws9c">para o quarto<span class="_d blank"> </span>quadran<span class="_7 blank"></span>te.<span class="_2a blank"> </span>H´<span class="_17 blank"></span><span class="ls6a ws9d">a5<span class="_b blank"></span><span class="ff3 ls67">×<span class="ff2 ls68">4</span>×<span class="ff2 ls69">3</span>×<span class="ff2 ls74 ws9e">3<span class="_6 blank"> </span>=<span class="_6 blank"> </span>180<span class="_d blank"> </span>mo dos<span class="_8 blank"> </span>de<span class="_8 blank"> </span>colorir<span class="_d blank"> </span>o</span></span></span></div><div class="t m0 x0 h2 y53 ff2 fs1 fc0 sc0 ls29 ws9f">mapa usando cores iguais no<span class="_25 blank"> </span>primeiro e no terceiro quadran<span class="_7 blank"></span>tes.</div><div class="t m0 x0 h2 y54 ff2 fs1 fc0 sc0 ls26 wsa0">No total, temos, p<span class="_4 blank"> </span>ortan<span class="_7 blank"></span>to, 80<span class="_23 blank"> </span>+<span class="_23 blank"> </span>180<span class="_1e blank"> </span>=<span class="_1e blank"> </span>260 mo<span class="_4 blank"> </span>dos de<span class="_8 blank"> </span>colorir a \ufb01gura.</div><div class="t m0 x6 h2 y55 ff1 fs1 fc0 sc0 ls1b ws73">12) <span class="ff2 ls3b wsa1">a) H´<span class="_17 blank"></span><span class="ls6a ws9d">a2<span class="_19 blank"></span>6</span></span></div><div class="t m0 x7 h3 y56 ff4 fs2 fc0 sc0 ls6b">5<span class="ff2 fs1 ls75 wsa2 v1">=1<span class="_19 blank"></span>1<span class="_9 blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3 ws10">881</span>.<span class="ff2 ls76 wsa3">376 pala<span class="_7 blank"></span>vras de 5<span class="_d blank"> </span>letras.<span class="_2a blank"> </span>Delas,<span class="_d blank"> </span>dev<span class="_7 blank"></span>emos<span class="_d blank"> </span>subtrair</span></span></span></div><div class="t m0 x0 ha y57 ff2 fs1 fc0 sc0 ls3d wsa4">as pala<span class="_7 blank"></span>vras que come¸<span class="_11 blank"></span><span class="ls39 wsa5">cam<span class="_25 blank"> </span>p or<span class="_1e blank"> </span>A,<span class="_25 blank"> </span>1<span class="_2b blank"> </span><span class="ff3 ls6c">×</span><span class="ls3 ws10">26<span class="ff4 fs2 ls13 v3">4</span><span class="ws5d v0">= 456<span class="ff5 ls23 wsf">.</span><span class="ls26 wsa6">976, e aquelas nas quais</span></span></span></span></div><div class="t m0 x0 hb y58 ff2 fs1 fc0 sc0 ls32 wsa7">a letra A n\u02dc<span class="_10 blank"></span><span class="ls6d">ao \ufb01gura, 25<span class="ff4 fs2 ls13 v3">5</span><span class="ls22 wse v0">=9<span class="_c blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3 ws10">765</span>.<span class="ff2 ls3">625.</span></span></span></span></div><div class="t m0 x0 h2 y59 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e1<span class="_9 blank"></span>1<span class="_9 blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3 ws10">881</span>.<span class="ff2 ls3 wsa8">376 <span class="ff3 ls11">\u2212</span><span class="ws10">456</span></span>.<span class="ff2 ls3 wsa8">976 <span class="ff3 ls0">\u2212</span><span class="ls44">9</span></span>.<span class="ff2 ls3 ws10">765</span>.<span class="ff2 ls3 wsa9">625 = 1</span>.<span class="ff2 ls3 ws10">658</span>.<span class="ff2 ls3">775.</span></span></span></div><div class="t m0 x0 h2 y5a ff2 fs1 fc0 sc0 ls53 ws52">b)<span class="_d blank"> </span>O<span class="_d blank"> </span>n ´<span class="_3 blank"></span><span class="ls1b wsaa">umero total de pala<span class="_7 blank"></span>vras de 5 letras distin<span class="_7 blank"></span>tas<span class="_8 blank"> </span>´<span class="_10 blank"></span><span class="ls77 wsab">e2<span class="_19 blank"></span>6<span class="_2 blank"></span><span class="ff3 ls6e">×<span class="ff2 ls3 wsac">25 </span>×<span class="ff2 ls3 wsad">24 </span><span class="ls23">×</span></span></span></span></div><div class="t m0 x0 h2 y5b ff2 fs1 fc0 sc0 ls3 wsae">23 <span class="ff3 ls6f">×</span><span class="ws5d">22 = 7<span class="ff5 ls23 wsf">.</span><span class="ws10">893<span class="ff5 ls23 wsf">.</span><span class="ls6d wsaf">600.<span class="_20 blank"> </span>Delas dev<span class="_2c blank"></span>emos subtrair as palav<span class="_7 blank"></span>ras que come¸<span class="_10 blank"></span><span class="ls50 ws47">cam</span></span></span></span></div><div class="t m0 x0 h2 y5c ff2 fs1 fc0 sc0 ls71 wsb0">po<span class="_7 blank"></span>r<span class="_25 blank"> </span>A,<span class="_25 blank"> </span>1 <span class="ff3 ls67">×</span><span class="ls3 wsb1">25 <span class="ff3 ls67">×</span>24 <span class="ff3 ls67">×</span>23 <span class="ff3 ls46">×</span><span class="wsb2">22 = 303<span class="ff5 ls23 wsf">.</span><span class="ls74 wsb3">600 e a<span class="_4 blank"> </span>quelas nas quais a<span class="_8 blank"> </span>letra<span class="_d blank"> </span>A</span></span></span></div><div class="t m0 x0 h2 y5d ff2 fs1 fc0 sc0 ls53 wsb4">n\u02dc<span class="_17 blank"></span><span class="ls6d wsb5">ao<span class="_6 blank"> </span>\ufb01gura,<span class="_6 blank"> </span>25 <span class="ff3 ls0">×</span><span class="ls3 wsb6">24 <span class="ff3 ls0">×</span><span class="wsb7">23 <span class="ff3 ls11">×</span>22 <span class="ff3 ls0">×</span><span class="ws5d">21 = 6<span class="ff5 ls23 wsf">.</span><span class="ws10">375<span class="ff5 ls23 wsf">.</span>600.</span></span></span></span></span></div><div class="t m0 x0 h2 y5e ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e7<span class="_9 blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3 ws10">893</span>.<span class="ff2 ls3 wsa8">600 <span class="ff3 ls0">\u2212</span><span class="ws10">303</span></span>.<span class="ff2 ls3 wsa8">600 <span class="ff3 ls11">\u2212</span><span class="ls44">6</span></span>.<span class="ff2 ls3 ws10">375</span>.<span class="ff2 ls3 ws5d">600 = 1</span>.<span class="ff2 ls3 ws10">214</span>.<span class="ff2 ls3">400.</span></span></span></div><div class="t m0 x0 h2 y5f ff1 fs1 fc0 sc0 ls2a ws18">Outra solu¸<span class="_17 blank"></span><span class="ls2b ws19">c\u02dc<span class="_3 blank"></span><span class="ls2c">ao:</span></span></div><div class="t m0 x5 h2 y41 ff2 fs1 fc0 sc0 ls23">3</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><div class="t m0 x0 h2 y0 ff2 fs1 fc0 sc0 ls3c ws95">H´<span class="_17 blank"></span><span class="ls7f wsb8">a4p<span class="_11 blank"></span>o<span class="_11 blank"></span>s<span class="_10 blank"></span>i<span class="_10 blank"></span>¸<span class="_18 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls61 wsb9">oes para colo<span class="_4 blank"> </span>car a letra A; depo<span class="_4 blank"> </span>is disso,<span class="_28 blank"> </span>as quatro c<span class="_7 blank"></span>asas</span></span></span></div><div class="t m0 x0 h2 y42 ff2 fs1 fc0 sc0 ls74 ws9e">v<span class="_2c blank"></span>azias<span class="_25 blank"> </span>p o dem<span class="_6 blank"> </span>ser<span class="_6 blank"> </span>preenc<span class="_2c blank"></span>hidas<span class="_8 blank"> </span>de<span class="_6 blank"> </span>25,<span class="_6 blank"> </span>24,<span class="_6 blank"> </span>23<span class="_6 blank"> </span>e<span class="_6 blank"> </span>22<span class="_6 blank"> </span>mo dos.</div><div class="t m0 x0 h2 y60 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e4<span class="_b blank"></span><span class="ff3 ls0">×<span class="ff2 ls3 wsb7">25 </span><span class="ls11">×<span class="ff2 ls3 wsb7">24 </span></span>×<span class="ff2 ls3 wsb6">23 </span>×<span class="ff2 ls3 ws2e">22 = 1<span class="ff5 ls23 wsf">.</span><span class="ws10">214<span class="ff5 ls23 wsf">.</span>400.</span></span></span></span></div><div class="t m0 x6 h2 y61 ff1 fs1 fc0 sc0 ls1b ws73">13) <span class="ff2 ls3c ws5b">Cada<span class="_d blank"> </span>letra<span class="_d blank"> </span>p o de<span class="_d blank"> </span>ser<span class="_d blank"> </span>escolhida<span class="_d blank"> </span>de<span class="_d blank"> </span>26<span class="_d blank"> </span>mo dos,<span class="_d blank"> </span>enquan<span class="_2c blank"></span>to<span class="_20 blank"> </span>cada<span class="_d blank"> </span>algarismo</span></div><div class="t m0 x0 h2 y62 ff2 fs1 fc0 sc0 ls23 ws2a">p o de<span class="_f blank"> </span>ser<span class="_e blank"> </span>escolhido<span class="_f blank"> </span>de<span class="_e blank"> </span>10<span class="_e blank"> </span>mo dos.<span class="_2d blank"> </span>Logo,<span class="_e blank"> </span>o<span class="_e blank"> </span>n ´<span class="_3 blank"></span><span class="ls8 wsba">umero total<span class="_e blank"> </span>de placas ´<span class="_11 blank"></span><span class="ls23">e</span></span></div><div class="t m0 x0 hc y63 ff2 fs1 fc0 sc0 ls3 ws10">26<span class="ff4 fs2 ls10 v3">3</span><span class="ff3 ls11 v0">×</span><span class="v0">10<span class="ff4 fs2 ls13 v3">4</span><span class="ws35">= 175<span class="ff5 ls23 wsf">.</span></span>760<span class="ff5 ls23 wsf">.</span>000.</span></div><div class="t m0 x6 h2 y64 ff1 fs1 fc0 sc0 ls1b ws73">14) <span class="ff2 ls35 wsbb">On<span class="_c blank"></span>´<span class="_2e blank"></span><span class="ls34 wsbc">umero de mo<span class="_4 blank"> </span>dos de acomo<span class="_4 blank"> </span>dar os passageiros qu<span class="_7 blank"></span>e pretendem<span class="_25 blank"> </span>sen<span class="_7 blank"></span>tar</span></span></div><div class="t m0 x0 h2 y65 ff2 fs1 fc0 sc0 ls24 wsbd">de frente ´<span class="_10 blank"></span><span class="ls80 wsbe">e5<span class="_b blank"></span><span class="ff3 ls6e">×<span class="ff2 ls68">4</span><span class="ls67">×<span class="ff2 ls68">3</span></span>×<span class="ff2 ls3 ws69">2<span class="_8 blank"> </span>=<span class="_8 blank"> </span>120;<span class="_d blank"> </span>o<span class="_8 blank"> </span>n ´<span class="_3 blank"></span><span class="ls60 wsbf">umero<span class="_d blank"> </span>de<span class="_8 blank"> </span>mo dos<span class="_d blank"> </span>de<span class="_8 blank"> </span>acomo dar<span class="_8 blank"> </span>os</span></span></span></span></div><div class="t m0 x0 h2 y66 ff2 fs1 fc0 sc0 ls40 wsc0">passageiros que pretendem sen<span class="_2c blank"></span>tar de costas<span class="_1e blank"> </span>´<span class="_10 blank"></span><span class="ls81 wsc1">e5<span class="_b blank"></span><span class="ff3 ls78">×<span class="ff2 ls79">4</span>×<span class="ff2 ls3 wsc2">3<span class="_1e blank"> </span>=<span class="_1d blank"> </span>60;<span class="_6 blank"> </span>o<span class="_25 blank"> </span>n ´<span class="_3 blank"></span><span class="ls53">umero</span></span></span></span></div><div class="t m0 x0 h2 y67 ff2 fs1 fc0 sc0 ls5f wsc3">de<span class="_6 blank"> </span>mo dos<span class="_25 blank"> </span>de<span class="_8 blank"> </span>acomo dar<span class="_25 blank"> </span>o s<span class="_25 blank"> </span>demais<span class="_6 blank"> </span>passageiros<span class="_1e blank"> </span>´<span class="_11 blank"></span><span class="ls38 ws2d">e3<span class="_b blank"></span><span class="ff3 ls11">×<span class="ff2 ls1">2</span><span class="ls0">×<span class="ff2 ls55 ws54">1=6<span class="_1b blank"></span>.</span></span></span></span></div><div class="t m0 x0 h2 y68 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls3 wsc4">e<span class="_25 blank"> </span>120 <span class="ff3 ls11">×</span><span class="wsb7">60 <span class="ff3 ls0">×</span><span class="ls55 ws54">6=<span class="_4 blank"> </span>4<span class="_c blank"></span>3<span class="_c blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3">200.</span></span></span></span></span></div><div class="t m0 x6 h2 y69 ff1 fs1 fc0 sc0 ls1b ws73">15) <span class="ff2 ls2f wsc5">V<span class="_b blank"></span>amos primeiramen<span class="_7 blank"></span>te<span class="_e blank"> </span>determinar quan<span class="_2c blank"></span>tos zeros s\u02dc<span class="_17 blank"></span><span class="ls2c wsc6">a<span class="_4 blank"> </span>o escritos na ca<span class="_4 blank"> </span>sa</span></span></div><div class="t m0 x0 h2 y6a ff2 fs1 fc0 sc0 ls2e wsc7">das unidades,<span class="_8 blank"> </span>dep<span class="_4 blank"> </span>ois na<span class="_8 blank"> </span>das dezenas,<span class="_8 blank"> </span>etc.</div><div class="t m0 x0 h2 y6b ff2 fs1 fc0 sc0 ls3c ws95">H´<span class="_17 blank"></span><span class="ls3 wsc8">a 222 n<span class="_4 blank"> </span>´<span class="_17 blank"></span><span class="ls3c wsc9">umeros que t<span class="_2c blank"></span>\u02c6<span class="_11 blank"></span>em 0 como algarismo das unidades,<span class="_6 blank"> </span>p<span class="_4 blank"> </span>ois an<span class="_7 blank"></span>tes do</span></span></div><div class="t m0 x0 h2 y6c ff2 fs1 fc0 sc0 ls82 ws52">zero<span class="_6 blank"> </span>p o dem<span class="_25 blank"> </span>ser<span class="_8 blank"> </span>colo cados<span class="_25 blank"> </span>os<span class="_6 blank"> </span>inte<span class="_7 blank"></span>iros<span class="_6 blank"> </span>de<span class="_8 blank"> </span>1<span class="_6 blank"> </span>(inclusiv<span class="_2c blank"></span>e)<span class="_8 blank"> </span>a<span class="_6 blank"> </span>222<span class="_6 blank"> </span>(inclusiv<span class="_2c blank"></span>e).</div><div class="t m0 x0 h2 y6d ff2 fs1 fc0 sc0 ls3c ws95">H´<span class="_17 blank"></span><span class="ls83 wsca">a2<span class="_14 blank"></span>2<span class="_2 blank"></span><span class="ff3 ls4d">×<span class="ff2 ls3 ws69">10<span class="_e blank"> </span>=<span class="_f blank"> </span>220<span class="_f blank"> </span>n ´<span class="_3 blank"></span><span class="ls3c wscb">umeros que<span class="_f blank"> </span>t\u02c6<span class="_10 blank"></span><span class="ls21">em 0 co<span class="_4 blank"> </span>mo a<span class="_4 blank"> </span>lgarismo das<span class="_e blank"> </span>dezenas,</span></span></span></span></span></div><div class="t m0 x0 h2 y6e ff2 fs1 fc0 sc0 ls61 wscc">p<span class="_4 blank"> </span>ois an<span class="_2c blank"></span>tes<span class="_25 blank"> </span>do zero p<span class="_1f blank"> </span>o<span class="_4 blank"> </span>dem ser colo<span class="_4 blank"> </span>cados os in<span class="_7 blank"></span>teiros de 1 (inclusiv<span class="_2c blank"></span>e)<span class="_6 blank"> </span>a 22</div><div class="t m0 x0 h2 y6f ff2 fs1 fc0 sc0 ls41 wscd">(inclusiv<span class="_2c blank"></span>e)<span class="_8 blank"> </span>e dep<span class="_4 blank"> </span>ois<span class="_8 blank"> </span>do zero, os inteiros de 0 (inclusiv<span class="_7 blank"></span>e)<span class="_8 blank"> </span>a 9 (inclusiv<span class="_7 blank"></span>e).</div><div class="t m0 x0 h2 y70 ff2 fs1 fc0 sc0 ls41 wsce">H´<span class="_17 blank"></span><span class="ls84 wscf">a2<span class="_2f blank"></span><span class="ff3 ls7a">×<span class="ff2 ls3 wsd0">100 = 200 n<span class="_4 blank"> </span>´<span class="_3 blank"></span><span class="ls3c wsd1">umeros que t\u02c6<span class="_10 blank"></span><span class="ls14 wsd2">em 0 como algarismo das cen<span class="_2c blank"></span>tenas,</span></span></span></span></span></div><div class="t m0 x0 h2 y71 ff2 fs1 fc0 sc0 ls61 wsd3">p<span class="_4 blank"> </span>ois an<span class="_2c blank"></span>tes do<span class="_8 blank"> </span>zero p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>dem ser colo<span class="_4 blank"> </span>cados os in<span class="_7 blank"></span>teiros de 1 (inclusiv<span class="_2c blank"></span>e)<span class="_8 blank"> </span>a 2</div><div class="t m0 x0 h2 y72 ff2 fs1 fc0 sc0 ls41 wsd4">(inclusiv<span class="_2c blank"></span>e)<span class="_25 blank"> </span>e dep<span class="_1f blank"> </span>ois do zero, os<span class="_25 blank"> </span>in<span class="_7 blank"></span>teiros de 0 (inclusive) a 99 (inclusive).</div><div class="t m0 x0 h2 y73 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls3 wsd5">e<span class="_25 blank"> </span>222 + 220 + 200<span class="_1e blank"> </span>=<span class="_1e blank"> </span>642.</span></div><div class="t m0 x6 hd y74 ff1 fs1 fc0 sc0 ls1b wsd6">16) <span class="ff2 ls23 v4">´</span></div><div class="t m0 x0 h2 y74 ff2 fs1 fc0 sc0 ls5 wsd7">E<span class="_20 blank"> </span>mais<span class="_f blank"> </span>simples<span class="_f blank"> </span>con<span class="_2c blank"></span>tar,<span class="_f blank"> </span>primeiramen<span class="_2c blank"></span>te,<span class="_e blank"> </span>os<span class="_f blank"> </span>n´<span class="_17 blank"></span><span class="ls4f wsd8">umeros onde o a<span class="_4 blank"> </span>lgarismo</span></div><div class="t m0 x0 h2 y75 ff2 fs1 fc0 sc0 ls85 wsd9">5n<span class="_19 blank"></span>\u02dc<span class="_1c blank"></span><span class="ls3e wsda">ao aparece.<span class="_2a blank"> </span>O primeiro d<span class="_2f blank"></span>´<span class="_19 blank"></span><span class="ls1c wsdb">\u0131gito<span class="_8 blank"> </span>p o de<span class="_8 blank"> </span>ser<span class="_d blank"> </span>escolhido<span class="_d blank"> </span>de<span class="_8 blank"> </span>8<span class="_8 blank"> </span>mo dos<span class="_d blank"> </span>(n\u02dc<span class="_17 blank"></span><span class="ls3">ao</span></span></span></div><div class="t m0 x0 h2 y76 ff2 fs1 fc0 sc0 ls24 wsdc">p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>de ser<span class="_20 blank"> </span>igual a<span class="_20 blank"> </span>0 nem<span class="_f blank"> </span>igual a 5) e cada<span class="_20 blank"> </span>um dos<span class="_20 blank"> </span>demais<span class="_20 blank"> </span>tr\u02c6<span class="_10 blank"></span><span class="ls50 wsdd">es d<span class="_2f blank"></span>´<span class="_19 blank"></span><span class="ls74">\u0131gitos</span></span></div><div class="t m0 x0 h2 y77 ff2 fs1 fc0 sc0 ls23 wsde">p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>de ser sele<span class="_7 blank"></span>cionado de 9 modos (dev<span class="_7 blank"></span>e ser diferen<span class="_2c blank"></span>te de 5).<span class="_26 blank"> </span>Logo, h´<span class="_3 blank"></span>a</div><div class="t m0 x0 he y78 ff2 fs1 fc0 sc0 ls7b">8<span class="ff3 ls7c">×</span><span class="ls7d">9<span class="ff4 fs2 ls4a v3">3</span><span class="ls22 wse v0">=5<span class="_c blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3 ws69">832<span class="_1d blank"> </span>n ´<span class="_3 blank"></span><span class="ls24 wsdf">umeros de 4 algarismos em<span class="_1d blank"> </span>que n\u02dc<span class="_17 blank"></span><span class="ls34 wse0">ao aparece o algarismo</span></span></span></span></span></span></div><div class="t m0 x0 h2 y79 ff2 fs1 fc0 sc0 ls3">5.</div><div class="t m0 x0 hf y7a ff2 fs1 fc0 sc0 ls86 wse1">Aq<span class="_22 blank"></span>u<span class="_22 blank"></span>a<span class="_22 blank"></span>n<span class="_c blank"></span>t<span class="_29 blank"></span>i<span class="_24 blank"></span>d<span class="_22 blank"></span>a<span class="_22 blank"></span>d<span class="_22 blank"></span>e d<span class="_22 blank"></span>e n<span class="_29 blank"></span>´<span class="_30 blank"></span><span class="ls24 wse2">umeros de 4 d<span class="_b blank"></span>´<span class="_1a blank"></span><span class="ls87 wse3">\u0131gitos,<span class="_1d blank"> </span>com ou sem<span class="_1d blank"> </span>o d<span class="_2f blank"></span>´<span class="_1a blank"></span><span class="ls61 wse4">\u0131gito 5, ´<span class="_11 blank"></span><span class="ls88 wse5">e9<span class="_22 blank"></span><span class="ff3 ls7e">×<span class="ff2 ls3 ws10">10<span class="ff4 fs2 ls4a v3">3</span><span class="ls23 v0">=</span></span></span></span></span></span></span></div><div class="t m0 x0 h2 y7b ff2 fs1 fc0 sc0 ls44">9<span class="ff5 ls23 wsf">.</span><span class="ls6d wse6">000<span class="_d blank"> </span>(p ois<span class="_20 blank"> </span>h´<span class="_17 blank"></span><span class="ls89 wse7">a9m<span class="_14 blank"></span>o<span class="_19 blank"></span>d<span class="_11 blank"></span>o<span class="_14 blank"></span>sd<span class="_14 blank"></span>es<span class="_14 blank"></span>e<span class="_14 blank"></span>l<span class="_14 blank"></span>e<span class="_14 blank"></span>c<span class="_14 blank"></span>i<span class="_14 blank"></span>o<span class="_14 blank"></span>n<span class="_14 blank"></span>a<span class="_1a blank"></span>rop<span class="_14 blank"></span>r<span class="_14 blank"></span>i<span class="_1a blank"></span>m<span class="_14 blank"></span>e<span class="_14 blank"></span>i<span class="_14 blank"></span>r<span class="_14 blank"></span>od<span class="_3 blank"></span>´<span class="_2e blank"></span><span class="ls3c wse8">\u0131gito,<span class="_f blank"> </span>que dev<span class="_2c blank"></span>e<span class="_f blank"> </span>ser</span></span></span></div><div class="t m0 x0 h2 y7c ff2 fs1 fc0 sc0 ls24 wse9">diferen<span class="_2c blank"></span>te<span class="_25 blank"> </span>de 0, e 10 mo<span class="_1f blank"> </span>dos de selecionar cada um dos demais 4 d<span class="_2f blank"></span>´<span class="_1a blank"></span><span class="ls4f">\u0131gitos).</span></div><div class="t m0 x0 h2 y7d ff2 fs1 fc0 sc0 ls34 wsea">Logo, h´<span class="_17 blank"></span><span class="ls8a wseb">a9<span class="_1a blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3 wsec">000 <span class="ff3 ls65">\u2212</span><span class="ls44">5</span></span>.<span class="ff2 ls3 wsed">832 = 3</span>.<span class="ff2 ls3 ws69">168<span class="_d blank"> </span>n ´<span class="_17 blank"></span><span class="ls56 ws8a">umeros de 4<span class="_20 blank"> </span>algarismos em<span class="_20 blank"> </span>que o<span class="_20 blank"> </span>5</span></span></span></span></div><div class="t m0 x0 h2 y7e ff2 fs1 fc0 sc0 ls53 wsb4">n\u02dc<span class="_17 blank"></span><span class="ls50 ws3d">ao a<span class="_4 blank"> </span>parece.</span></div><div class="t m0 x5 h2 y7f ff2 fs1 fc0 sc0 ls23">4</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><div class="t m0 x6 h2 y0 ff1 fs1 fc0 sc0 ls1b ws73">17) <span class="ff2 ls57 ws90">Dev<span class="_7 blank"></span>emos decidir<span class="_8 blank"> </span>quan<span class="_7 blank"></span>tos exemplares<span class="_8 blank"> </span>de ca<span class="_4 blank"> </span>da revista dev<span class="_7 blank"></span>em ser p<span class="_1f blank"> </span>ostos</span></div><div class="t m0 x0 h2 y42 ff2 fs1 fc0 sc0 ls52 wsee">na cole¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls74 wsef">ao. H´<span class="_17 blank"></span><span class="ls8 wsf0">a 6 p<span class="_4 blank"> </span>ossibilidades<span class="_28 blank"> </span>para a<span class="_f blank"> </span>\u201dV<span class="_2c blank"></span>e<span class="_7 blank"></span>ja\u201d (0,<span class="_28 blank"> </span>1, 2,<span class="_28 blank"> </span>3,<span class="_28 blank"> </span>4,<span class="_28 blank"> </span>ou 5</span></span></span></div><div class="t m0 x0 hd y80 ff2 fs1 fc0 sc0 ls28 wsf1">exemplares),<span class="_d blank"> </span>7 pa<span class="_4 blank"> </span>ra a \u201dManc<span class="_2c blank"></span>hete\u201d<span class="_d blank"> </span>e 5 para a \u201d<span class="_4 blank"> </span>Isto<span class="_f blank"> </span><span class="ls23 v4">´</span></div><div class="t m0 x8 h2 y80 ff2 fs1 fc0 sc0 lsa2 wsdb">E\u201d.<span class="_2a blank"> </span>O<span class="_d blank"> </span>n ´<span class="_3 blank"></span><span class="ls53 wsf2">umero de</span></div><div class="t m0 x0 h2 y81 ff2 fs1 fc0 sc0 ls1d wsf3">cole¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls3 wsf4">oes ´<span class="_10 blank"></span><span class="ls38 ws2d">e6<span class="_b blank"></span><span class="ff3 ls11">×<span class="ff2 ls1">7</span><span class="ls0">×<span class="ff2 ls3 ws69">5<span class="_1e blank"> </span>=<span class="_1e blank"> </span>210,<span class="_25 blank"> </span>e<span class="_6 blank"> </span>o<span class="_8 blank"> </span>n ´<span class="_3 blank"></span><span class="ls39 wsf5">umero de cole¸<span class="_14 blank"></span><span class="ls50 ws47">c\u02dc<span class="_17 blank"></span><span class="ls3 wsf6">oes n\u02dc<span class="_17 blank"></span><span class="lsa3 wsf7">ao-v<span class="_2c blank"></span>azias ´<span class="_10 blank"></span><span class="ls3 wsf8">e 209.</span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x6 h2 y82 ff1 fs1 fc0 sc0 ls1b ws73">18) <span class="ff2 ls32 wsf9">Em cada dia,<span class="_28 blank"> </span>duas<span class="_28 blank"> </span>das mat<span class="_2c blank"></span>´<span class="_11 blank"></span><span class="ls3c wsfa">erias s\u02dc<span class="_3 blank"></span><span class="ls3b wsfb">ao ensinadas e uma folga.<span class="_31 blank"> </span>H´<span class="_17 blank"></span><span class="lsa4">a3</span></span></span></span></div><div class="t m0 x0 h2 y83 ff2 fs1 fc0 sc0 ls2d wsfc">p<span class="_4 blank"> </span>ossibilidades<span class="_e blank"> </span>para escolher a mat´<span class="_10 blank"></span><span class="ls56 wsfd">eria que<span class="_e blank"> </span>folga na segunda,<span class="_32 blank"> </span>2 para</span></div><div class="t m0 x0 h2 y84 ff2 fs1 fc0 sc0 ls28 wsf1">escolher a que fo<span class="_4 blank"> </span>lga na quarta e 1 para escolher a que f<span class="_4 blank"> </span>olga na sexta.</div><div class="t m0 x0 h2 y85 ff2 fs1 fc0 sc0 ls14 wsfe">P<span class="_2c blank"></span>ortanto, h´<span class="_3 blank"></span><span class="ls39 wsff">a 6 mo<span class="_1f blank"> </span>dos para escolher<span class="_e blank"> </span>a<span class="_4 blank"> </span>s mat´<span class="_17 blank"></span><span class="ls5 ws100">erias<span class="_e blank"> </span>de cada dia.<span class="_33 blank"> </span>P<span class="_2c blank"></span>ara</span></span></div><div class="t m0 x0 h2 y86 ff2 fs1 fc0 sc0 ls2e ws101">escolher o<span class="_4 blank"> </span>s hor´<span class="_17 blank"></span><span class="ls23 ws102">arios, h´<span class="_10 blank"></span><span class="ls2f ws103">a 2 p<span class="_4 blank"> </span>ossibilidades em cada dia.<span class="_e blank"> </span>Logo, o n<span class="_4 blank"> </span>´<span class="_3 blank"></span><span class="ls53">umero</span></span></span></div><div class="t m0 x0 h2 y87 ff2 fs1 fc0 sc0 ls87 ws104">total de hor´<span class="_17 blank"></span><span class="ls60 ws105">arios ´<span class="_11 blank"></span><span class="ls1f wsa">e6<span class="_2f blank"></span><span class="ff3 ls0">×<span class="ff2 ls3 wsb2">8 = 48.</span></span></span></span></div><div class="t m0 x6 h2 y88 ff1 fs1 fc0 sc0 ls1b ws73">19) <span class="ff2 ls37 ws106">F<span class="_b blank"></span>o<span class="_4 blank"> </span>i feita<span class="_8 blank"> </span>uma<span class="_d blank"> </span>distin¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_17 blank"></span><span class="ls5 ws107">ao<span class="_d blank"> </span>arti\ufb01cial ao se considerar cada casal ordenado</span></span></span></div><div class="t m0 x0 h2 y89 ff2 fs1 fc0 sc0 ls52 ws108">de<span class="_1e blank"> </span>dois<span class="_25 blank"> </span>mo dos<span class="_1e blank"> </span>diferentes:<span class="_f blank"> </span>come¸<span class="_11 blank"></span><span class="ls41 ws109">cando p<span class="_1f blank"> </span>ela m<span class="_2c blank"></span>ulher<span class="_25 blank"> </span>ou p<span class="_1f blank"> </span>elo homem.<span class="_20 blank"> </span>Por</span></div><div class="t m0 x0 h2 y8a ff2 fs1 fc0 sc0 ls41 ws10a">esta raz\u02dc<span class="_17 blank"></span><span class="ls82 ws10b">ao, o resultado<span class="_8 blank"> </span>encon<span class="_7 blank"></span>trado foi igual ao<span class="_8 blank"> </span>dobro do correto.</span></div><div class="t m0 x6 h2 y8b ff1 fs1 fc0 sc0 ls1b ws73">20) <span class="ff2 ls3c ws95">H´<span class="_17 blank"></span><span class="ls7f wsb8">at<span class="_11 blank"></span>r<span class="_3 blank"></span>\u02c6<span class="_18 blank"></span><span class="ls1b ws10c">es<span class="_e blank"> </span>tip os<span class="_e blank"> </span>de<span class="_e blank"> </span>cart\u02dc<span class="_17 blank"></span><span class="ls34 ws10d">oes:<span class="_34 blank"> </span>os que virados de cab<span class="_4 blank"> </span>e¸<span class="_11 blank"></span><span class="ls3f ws10e">ca para baixo<span class="_32 blank"> </span>n\u02dc<span class="_17 blank"></span><span class="ls3">ao</span></span></span></span></span></span></div><div class="t m0 x0 h2 y8c ff2 fs1 fc0 sc0 ls2a ws10f">represen<span class="_2c blank"></span>ta m<span class="_20 blank"> </span>n ´<span class="_17 blank"></span><span class="ls60 ws110">umeros, como, por<span class="_20 blank"> </span>exemplo, 41.809; os qu<span class="_7 blank"></span>e v<span class="_7 blank"></span>irados de</span></div><div class="t m0 x0 h2 y8d ff2 fs1 fc0 sc0 ls50 ws111">cab e¸<span class="_11 blank"></span><span class="ls57 ws112">ca para baixo<span class="_32 blank"> </span>representam o mesmo n<span class="_4 blank"> </span>´<span class="_17 blank"></span><span class="ls1d ws6f">umero,<span class="_28 blank"> </span>como ,<span class="_28 blank"> </span>p or<span class="_32 blank"> </span>exem-</span></span></div><div class="t m0 x0 h2 y8e ff2 fs1 fc0 sc0 ls74 ws113">plo, 86.198; os que virados de cabe¸<span class="_11 blank"></span><span class="ls3c ws25">ca para baixo represen<span class="_7 blank"></span>tam n<span class="_4 blank"> </span>´<span class="_17 blank"></span><span class="ls2f">umeros</span></span></div><div class="t m0 x0 h2 y8f ff2 fs1 fc0 sc0 ls3d ws114">diferen<span class="_2c blank"></span>tes, como,<span class="_8 blank"> </span>p<span class="_4 blank"> </span>or exe<span class="_7 blank"></span>mplo, 66.810.<span class="_2a blank"> </span>Os c<span class="_7 blank"></span>art\u02dc<span class="_17 blank"></span><span class="ls3 ws115">oes do ´<span class="_17 blank"></span><span class="ls37 ws116">ultimo tip<span class="_4 blank"> </span>o s\u02dc<span class="_10 blank"></span><span class="ls3">ao</span></span></span></div><div class="t m0 x0 h2 y90 ff2 fs1 fc0 sc0 ls2e ws5c">os<span class="_20 blank"> </span>que<span class="_d blank"> </span>p ermitem<span class="_f blank"> </span>economia<span class="_20 blank"> </span>p orque<span class="_20 blank"> </span>um<span class="_20 blank"> </span>mesmo<span class="_f blank"> </span>cart\u02dc<span class="_17 blank"></span><span class="ls87 ws117">ao serv<span class="_2c blank"></span>e<span class="_20 blank"> </span>para<span class="_20 blank"> </span>rep-</span></div><div class="t m0 x0 h2 y91 ff2 fs1 fc0 sc0 ls23 ws2a">resen<span class="_2c blank"></span>tar<span class="_32 blank"> </span>dois<span class="_e blank"> </span>n ´<span class="_3 blank"></span><span class="ls52 ws118">umeros. H´<span class="_17 blank"></span><span class="ls7f wsb8">a5<span class="_2 blank"></span><span class="ff3 ls8b">×<span class="ff2 ls8c">5</span>×<span class="ff2 ls8c">5</span>×<span class="ff2 ls8c">5</span>×<span class="ff2 ls8d ws119">5=3<span class="_3 blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls87 ws11a">125 cart\u02dc<span class="_10 blank"></span><span class="ls61 ws11b">oes que</span></span></span></span></span></span></span></div><div class="t m0 x0 h2 y92 ff2 fs1 fc0 sc0 ls70 ws57">virados<span class="_e blank"> </span>de<span class="_e blank"> </span>cab e¸<span class="_11 blank"></span><span class="ls3c ws11c">ca para baixo representam n<span class="_4 blank"> </span>´<span class="_3 blank"></span><span class="ls5 ws11d">umeros,<span class="_32 blank"> </span>iguais ou difer-</span></span></div><div class="t m0 x0 h2 y93 ff2 fs1 fc0 sc0 ls76 ws11e">en<span class="_2c blank"></span>tes,<span class="_e blank"> </span>p ois<span class="_20 blank"> </span>tais<span class="_20 blank"> </span>cart\u02dc<span class="_10 blank"></span><span class="ls74 ws11f">oes dev<span class="_2c blank"></span>em<span class="_f blank"> </span>ter como algarismos apenas 0,<span class="_f blank"> </span>1,<span class="_f blank"> </span>8,<span class="_f blank"> </span>6</span></div><div class="t m0 x0 h2 y94 ff2 fs1 fc0 sc0 lsa5 ws120">ou<span class="_8 blank"> </span>9.<span class="_28 blank"> </span>Destes<span class="_7 blank"></span>,<span class="_d blank"> </span>5 <span class="ff3 ls67">×</span><span class="ls69">5<span class="ff3 ls67">×</span><span class="lsa6 ws121">3=7<span class="_9 blank"></span>5 s<span class="_9 blank"></span>\u02dc<span class="_1c blank"></span><span class="lsa7 ws122">ao<span class="_8 blank"> </span>do<span class="_d blank"> </span>segundo<span class="_8 blank"> </span>tip o,<span class="_d blank"> </span>p ois<span class="_8 blank"> </span>um<span class="_8 blank"> </span>tal<span class="_8 blank"> </span>cart\u02dc<span class="_17 blank"></span><span class="ls3">ao</span></span></span></span></div><div class="t m0 x0 h2 y95 ff2 fs1 fc0 sc0 ls60 ws123">dev<span class="_2c blank"></span>e<span class="_20 blank"> </span>ter as casas das extre<span class="_7 blank"></span>midades preenc<span class="_2c blank"></span>hidas<span class="_20 blank"> </span>p<span class="_4 blank"> </span>or 00, 11,<span class="_20 blank"> </span>88, 69 ou</div><div class="t m0 x0 h2 y96 ff2 fs1 fc0 sc0 ls3b ws124">96, a segunda e a quarta<span class="_1d blank"> </span>casas<span class="_25 blank"> </span>preenc<span class="_7 blank"></span>hidas p<span class="_4 blank"> </span>or 00, 11, 88, 69 ou 96, e a</div><div class="t m0 x0 h2 y97 ff2 fs1 fc0 sc0 ls52 ws125">casa cen<span class="_7 blank"></span>tral preenchida p<span class="_4 blank"> </span>or 0, 1 ou 8.<span class="_f blank"> </span>Portan<span class="_2c blank"></span>to,<span class="_8 blank"> </span>os cart\u02dc<span class="_10 blank"></span><span class="ls41 ws126">oes do terceiro</span></div><div class="t m0 x0 h2 y98 ff2 fs1 fc0 sc0 ls40 ws127">tip o<span class="_f blank"> </span>s\u02dc<span class="_17 blank"></span><span class="ls3 ws69">ao<span class="_f blank"> </span>em<span class="_f blank"> </span>n ´<span class="_17 blank"></span><span class="ls53 ws128">umero de 3<span class="ff5 ls23 wsf">.</span><span class="ls3 ws129">125 <span class="ff3 ls4d">\u2212</span><span class="ws12a">75 =<span class="_e blank"> </span>3<span class="ff5 ls23 wsf">.</span><span class="ls5f wsc3">050.<span class="_35 blank"> </span>P<span class="_2c blank"></span>o dem<span class="_e blank"> </span>ser<span class="_20 blank"> </span>economiza-</span></span></span></span></span></div><div class="t m0 x0 h2 y99 ff2 fs1 fc0 sc0 ls61 ws12b">dos 3<span class="ff5 ls23 wsf">.</span><span class="ls3 ws10">050<span class="ff5 ls44">/</span><span class="ls85 wsd9">2=1<span class="_19 blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls87 ws12c">525 cart\u02dc<span class="_17 blank"></span><span class="ls3 ws69">oes.<span class="_16 blank"> </span>O<span class="_d blank"> </span>n ´<span class="_3 blank"></span><span class="ls53 ws12d">umero m<span class="_b blank"></span>´<span class="_1a blank"></span><span class="ls1b ws12e">\u0131nimo<span class="_d blank"> </span>de cart\u02dc<span class="_10 blank"></span><span class="ls61 ws12b">oes de que se</span></span></span></span></span></span></span></span></div><div class="t m0 x0 h2 y9a ff2 fs1 fc0 sc0 ls39 ws12f">necessita ´<span class="_10 blank"></span><span class="ls3 ws34">e 100<span class="ff5 ls23 wsf">.</span><span class="wsa8">000 <span class="ff3 ls0">\u2212</span><span class="ls44">1<span class="ff5 ls23 wsf">.</span></span><span class="wsa9">525 =<span class="_1e blank"> </span>98<span class="ff5 ls23 wsf">.</span>475.</span></span></span></div><div class="t m0 x6 h10 y9b ff1 fs1 fc0 sc0 ls1b ws73">21) <span class="ff2 ls2c ws130">A<span class="_1e blank"> </span>decomp osi¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls61 ws131">ao<span class="_1e blank"> </span>de<span class="_1e blank"> </span>360<span class="_1e blank"> </span>em<span class="_1e blank"> </span>fatores<span class="_1e blank"> </span>primos ´<span class="_10 blank"></span><span class="ls3 ws132">e 720 =<span class="_25 blank"> </span>2<span class="ff4 fs2 ls49 v3">3</span><span class="ff5 ls23 wsf v0">.<span class="ff2 lsd">3<span class="ff4 fs2 ls49 v3">2</span></span>.<span class="ff2 ls5f ws133">5.<span class="_20 blank"> </span>Os divisores</span></span></span></span></span></span></div><div class="t m0 x0 h5 y9c ff2 fs1 fc0 sc0 ls5f ws134">in<span class="_2c blank"></span>teiros<span class="_6 blank"> </span>e<span class="_8 blank"> </span>p ositiv<span class="_2c blank"></span>os<span class="_8 blank"> </span>de<span class="_6 blank"> </span>720<span class="_6 blank"> </span>s\u02dc<span class="_17 blank"></span><span class="ls3 ws69">ao<span class="_6 blank"> </span>os<span class="_6 blank"> </span>n ´<span class="_3 blank"></span><span class="ls32 ws135">umeros da<span class="_8 blank"> </span>forma 2<span class="ff6 fs2 ls8e v3">\u03b1</span><span class="ff5 ls23 wsf v0">.<span class="ff2 lsd">3<span class="ff6 fs2 ls8f v3">\u03b2</span></span>.<span class="ff2 lsd">5<span class="ff6 fs2 ls90 v3">\u03b3</span><span class="lsa8 ws136">,c<span class="_19 blank"></span>o<span class="_9 blank"></span>m<span class="ff5 ls91">\u03b1<span class="ff3 ls23">\u2208</span></span></span></span></span></span></span></div><div class="t m0 x0 h2 y9d ff3 fs1 fc0 sc0 ls92">{<span class="ff2 ls44">0<span class="ff5 ls62">,</span>1<span class="ff5 ls62">,</span>2<span class="ff5 ls62">,</span>3</span>}<span class="ff2 ls93">,<span class="ff5 ls94">\u03b2</span></span><span class="lsa9 ws137">\u2208{<span class="_10 blank"></span><span class="ff2 ls44">0<span class="ff5 ls62">,</span>1<span class="ff5 ls62">,</span>2<span class="ff3 ls95">}</span><span class="ls96">e<span class="ff5 ls97">\u03b3<span class="ff3 lsa9">\u2208{<span class="_10 blank"></span><span class="ff2 ls44">0<span class="ff5 ls62">,</span>1<span class="ff3 ls92">}</span><span class="ls52 ws138">.<span class="_13 blank"> </span>A<span class="_f blank"> </span>soma<span class="_f blank"> </span>dos<span class="_e blank"> </span>divisores ´<span class="_10 blank"></span><span class="ls96">e<span class="ff5 ls98">S</span><span class="ls23">=</span></span></span></span></span></span></span></span></span></div><div class="t m0 x0 h11 y9e ff2 fs1 fc0 sc0 lsaa ws139">\u03a32<span class="ff6 fs2 ls8e v3">\u03b1</span><span class="ff5 ls23 wsf v0">.<span class="ff2 lsd">3<span class="ff6 fs2 ls8f v3">\u03b2</span></span>.<span class="ff2 lsd">5<span class="ff6 fs2 ls90 v3">\u03b3</span><span class="lsab ws13a">,c<span class="_1b blank"></span>o<span class="_c blank"></span>m<span class="ff5 ls99">\u03b1<span class="ff3 lsac ws13b">\u2208{<span class="_c blank"></span><span class="ff2 ls44">0<span class="ff5 ls62">,</span>1<span class="ff5 ls62">,</span>2<span class="ff5 ls62">,</span>3<span class="ff3 ls92">}</span><span class="ls9a">,<span class="ff5 ls9b">\u03b2<span class="ff3 lsac">\u2208{<span class="_c blank"></span><span class="ff2 ls44">0<span class="ff5 ls62">,</span>1<span class="ff5 ls62">,</span>2<span class="ff3 ls9c">}</span><span class="ls9d">e<span class="ff5 ls9e">\u03b3<span class="ff3 lsad ws13c">\u2208{<span class="_1b blank"></span><span class="ff2 ls44">0<span class="ff5 ls62">,</span>1<span class="ff3 ls92">}</span><span class="ls74 ws13d">.<span class="_20 blank"> </span>P<span class="_2c blank"></span>ara calcular</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x0 h2 y9f ff2 fs1 fc0 sc0 ls3b ws13e">essa soma,<span class="_1d blank"> </span>dividimos as parcelas em<span class="_1d blank"> </span>dois grupos,<span class="_1d blank"> </span>conforme seja <span class="ff5 ls9f">\u03b3</span><span class="lsae ws13f">=0<span class="_2c blank"></span>o<span class="_1b blank"></span>u</span></div><div class="t m0 x0 h2 ya0 ff5 fs1 fc0 sc0 ls9f">\u03b3<span class="ff2 ls35 ws140">=1<span class="_1b blank"></span>. <span class="ff5 lsa0">S</span><span class="lsae ws13f">=\u03a3<span class="_2f blank"></span>(<span class="_1b blank"></span>2</span></span></div><div class="t m0 x9 h4 ya1 ff6 fs2 fc0 sc0 lsa1">\u03b1<span class="ff5 fs1 ls23 wsf v1">.<span class="ff2 lsd">3</span></span><span class="ls8f">\u03b2<span class="ff5 fs1 ls23 wsf v1">.<span class="ff2 lsd">5</span></span><span class="ff4 ls49">0<span class="ff2 fs1 lsaf ws141 v1">)+\u03a3<span class="_b blank"></span>(<span class="_22 blank"></span>2</span></span></span></div><div class="t m0 xa h4 ya1 ff6 fs2 fc0 sc0 ls8e">\u03b1<span class="ff5 fs1 ls23 wsf v1">.<span class="ff2 lsd">3</span></span><span class="ls8f">\u03b2<span class="ff5 fs1 ls23 wsf v1">.<span class="ff2 lsd">5</span></span><span class="ff4 ls49">1<span class="ff2 fs1 lsb0 ws142 v1">)=6<span class="_2 blank"></span>\u03a3<span class="_2f blank"></span>(<span class="_1b blank"></span>2</span></span></span></div><div class="t m0 xb h4 ya1 ff6 fs2 fc0 sc0 ls8e">\u03b1<span class="ff5 fs1 ls23 wsf v1">.<span class="ff2 lsd">3</span></span><span class="ls8f">\u03b2<span class="ff2 fs1 ls1c ws143 v1">)<span class="_6 blank"> </span>p orque<span class="_8 blank"> </span>a<span class="_6 blank"> </span>segunda</span></span></div><div class="t m0 x5 h2 ya2 ff2 fs1 fc0 sc0 ls23">5</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><div class="t m0 x0 h2 y0 ff2 fs1 fc0 sc0 lsba ws144">soma ´<span class="_11 blank"></span><span class="lsb9 ws145">e igual ao qu<span class="_2f blank"></span>´<span class="_1a blank"></span><span class="ls5 ws146">\u0131ntuplo da primeira.<span class="_21 blank"> </span>Agora, dividimos as parcelas</span></span></div><div class="t m0 x0 h2 y42 ff2 fs1 fc0 sc0 ls34 ws147">em<span class="_8 blank"> </span>grup os,<span class="_d blank"> </span>conforme<span class="_8 blank"> </span>seja<span class="_8 blank"> </span><span class="ff5 lsb1">\u03b2</span><span class="ls75 ws148">=0<span class="_9 blank"></span>, <span class="ff5 lsb1">\u03b2</span><span class="ws149">=1 o<span class="_19 blank"></span>u <span class="ff5 lsb1">\u03b2</span><span class="lsbb ws140">=2<span class="_9 blank"></span>. <span class="ff5 lsb2">S</span><span class="ls75 wsa2">=6<span class="_29 blank"></span>[<span class="_9 blank"></span>\u03a3<span class="_29 blank"></span>(<span class="_19 blank"></span>2</span></span></span></span></div><div class="t m0 xc h4 ya3 ff6 fs2 fc0 sc0 ls8e">\u03b1<span class="ff5 fs1 ls23 wsf v1">.<span class="ff2 lsd">3</span></span><span class="ff4 ls49">0<span class="ff2 fs1 lsbc v1">)+</span></span></div><div class="t m0 x0 h2 ya4 ff2 fs1 fc0 sc0 lsb3 ws14a">\u03a3(<span class="_36 blank"></span>2</div><div class="t m0 xd h4 ya5 ff6 fs2 fc0 sc0 ls8e">\u03b1<span class="ff5 fs1 ls23 wsf v1">.<span class="ff2 lsd">3</span></span><span class="ff4 ls49">1<span class="ff2 fs1 lsb4 ws14b v1">)+\u03a3 (<span class="_2 blank"></span>2</span></span></div><div class="t m0 xe h4 ya5 ff6 fs2 fc0 sc0 lsa1">\u03b1<span class="ff5 fs1 ls23 wsf v1">.<span class="ff2 lsd">3</span></span><span class="ff4 ls49">2<span class="ff2 fs1 ls40 ws14c v1">)]<span class="_1e blank"> </span>=<span class="_1e blank"> </span>6[\u03a3 2</span></span><span class="lsb5">\u03b1<span class="ff2 fs1 lsbd ws14d v1">+3<span class="_2f blank"></span>\u03a3 2</span></span></div><div class="t m0 xf h4 ya5 ff6 fs2 fc0 sc0 lsb6">\u03b1<span class="ff2 fs1 lsbd ws14d v1">+9<span class="_2 blank"></span>\u03a3 2</span></div><div class="t m0 x10 h4 ya5 ff6 fs2 fc0 sc0 ls8e">\u03b1<span class="ff2 fs1 lsb9 ws14e v1">]<span class="_1e blank"> </span>=<span class="_1e blank"> </span>6[13\u03a3 2</span>\u03b1<span class="ff2 fs1 ls3 ws14f v1">] = 78\u03a32</span><span class="lsb7">\u03b1<span class="ff2 fs1 ls23 v1">=</span></span></div><div class="t m0 x0 h12 ya6 ff2 fs1 fc0 sc0 ls3d ws150">78[2<span class="ff4 fs2 ls10 v3">0</span><span class="lsbe v0">+2</span></div><div class="t m0 x7 h3 ya7 ff4 fs2 fc0 sc0 ls10">1<span class="ff2 fs1 lsbe v1">+2</span></div><div class="t m0 x11 h3 ya7 ff4 fs2 fc0 sc0 ls10">2<span class="ff2 fs1 lsbe v1">+2</span></div><div class="t m0 x12 h3 ya7 ff4 fs2 fc0 sc0 lsc">3<span class="ff2 fs1 lsbf ws151 v1">]=7<span class="_c blank"></span>8<span class="_2c blank"></span><span class="ff3 ls11">×<span class="ff2 ls3 ws2e">15 =<span class="_1e blank"> </span>1<span class="ff5 ls23 wsf">.</span>170.</span></span></span></div><div class="t m0 x0 h1 ya8 ff1 fs0 fc0 sc0 ls15 ws0">Solu¸<span class="_0 blank"></span><span class="ls16 ws1">c\u02dc<span class="_1 blank"></span><span class="ls17 ws2">oes dos Exerc<span class="_2 blank"></span>´<span class="_3 blank"></span><span class="ls18 ws3">\u0131cios da S<span class="_4 blank"> </span>e¸<span class="_0 blank"></span><span class="ls19 ws4">c\u02dc<span class="_5 blank"></span><span class="ls1a ws5">ao 4.2</span></span></span></span></span></div><div class="t m0 x1 h2 ya9 ff1 fs1 fc0 sc0 ls1b ws6">1) <span class="ff2 ls3 ws69">a)<span class="_25 blank"> </span>O<span class="_6 blank"> </span>n ´<span class="_17 blank"></span><span class="ls34 ws152">umero<span class="_6 blank"> </span>total<span class="_6 blank"> </span>de<span class="_6 blank"> </span>anagramas ´<span class="_11 blank"></span><span class="ls38 ws2d">e8<span class="_19 blank"></span>!<span class="_2c blank"></span>=<span class="_2c blank"></span>4<span class="_9 blank"></span>0<span class="_9 blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3">320.</span></span></span></span></span></div><div class="t m0 x0 h2 yaa ff2 fs1 fc0 sc0 ls52 ws94">b) H´<span class="_17 blank"></span><span class="ls5f ws153">a 4 mo<span class="_4 blank"> </span>dos de<span class="_1d blank"> </span>escolhe<span class="_7 blank"></span>r<span class="_1d blank"> </span>a v<span class="_2c blank"></span>ogal que ser´<span class="_17 blank"></span><span class="ls61 ws154">a<span class="_1d blank"> </span>a primeira letra do anagrama</span></span></div><div class="t m0 x0 h2 yab ff2 fs1 fc0 sc0 lsc0 wsa3">e 3 mo<span class="_4 blank"> </span>dos de sele<span class="_7 blank"></span>cionar a v<span class="_2c blank"></span>ogal que ser´<span class="_17 blank"></span><span class="ls6a ws155">aa ´<span class="_37 blank"></span><span class="ls8 ws156">ultima letra do anagrama.</span></span></div><div class="t m0 x0 h2 yac ff2 fs1 fc0 sc0 ls21 ws81">Dep ois<span class="_1e blank"> </span>disso,<span class="_25 blank"> </span>h´<span class="_17 blank"></span><span class="lsa7 ws157">a<span class="_1e blank"> </span>6!<span class="_f blank"> </span>modos de<span class="_1e blank"> </span>arrumar as<span class="_1e blank"> </span>demais<span class="_1e blank"> </span>letras en<span class="_7 blank"></span>tre a<span class="_1e blank"> </span>primeira</span></div><div class="t m0 x0 h2 yad ff2 fs1 fc0 sc0 ls38 ws24">ea ´<span class="_1c blank"></span><span class="ls76">ultima.</span></div><div class="t m0 x0 h2 yae ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e4<span class="_b blank"></span><span class="ff3 ls0">×<span class="ff2 ls1">3</span><span class="ls11">×<span class="ff2 ls3 wsa8">6!<span class="_1e blank"> </span>=<span class="_1e blank"> </span>4 </span></span>×<span class="ff2 ls1">3</span>×<span class="ff2 ls3 ws5d">720 = 8<span class="ff5 ls23 wsf">.</span>640.</span></span></span></div><div class="t m0 x0 h2 yaf ff2 fs1 fc0 sc0 ls29 ws158">c) As v<span class="_7 blank"></span>ogais e consoan<span class="_2c blank"></span>tes<span class="_20 blank"> </span>p<span class="_4 blank"> </span>o<span class="_1f blank"> </span>dem aparecer na ordem CV<span class="_d blank"> </span>CV<span class="_20 blank"> </span>CV CV</div><div class="t m0 x0 h2 yb0 ff2 fs1 fc0 sc0 ls57 ws159">ou na ordem V<span class="_2c blank"></span>C VC V<span class="_2c blank"></span>C V<span class="_7 blank"></span>C. No primeiro caso, devemos colo<span class="_4 blank"> </span>ca<span class="_4 blank"> </span>r as 4</div><div class="t m0 x0 h2 yb1 ff2 fs1 fc0 sc0 ls3d ws15a">v<span class="_2c blank"></span>ogais nos 4 lugares de orde<span class="_7 blank"></span>m par (4!<span class="_e blank"> </span>mo<span class="_4 blank"> </span>dos) e as 4 cons<span class="_7 blank"></span>oan<span class="_2c blank"></span>tes nos 4</div><div class="t m0 x0 h2 yb2 ff2 fs1 fc0 sc0 lsa7 ws15b">lugares<span class="_6 blank"> </span>de<span class="_6 blank"> </span>ordem ´<span class="_19 blank"></span><span class="ls76 ws81">\u0131mpar<span class="_25 blank"> </span>(4!<span class="_f blank"> </span>mo dos).</span></div><div class="t m0 x0 h2 yb3 ff2 fs1 fc0 sc0 ls3c ws95">H´<span class="_17 blank"></span><span class="lsc1 ws15c">a4<span class="_24 blank"></span>!<span class="_36 blank"></span><span class="ff3 lsb8">×<span class="ff2 ls3 ws15d">4!<span class="_1e blank"> </span>=<span class="_1e blank"> </span>24 </span>×<span class="ff2 ls74 ws15e">24 = 576 anagramas do primeiro tip<span class="_4 blank"> </span>o.<span class="_f blank"> </span>Analogamen<span class="_2c blank"></span>te,</span></span></span></div><div class="t m0 x0 h2 yb4 ff2 fs1 fc0 sc0 ls53 wsb4">h´<span class="_17 blank"></span><span class="ls4f ws15f">a 576 anagramas do segundo<span class="_8 blank"> </span>tip<span class="_4 blank"> </span>o.</span></div><div class="t m0 x0 h2 yb5 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls3 wsd5">e<span class="_25 blank"> </span>576 + 576<span class="_1e blank"> </span>=<span class="_1e blank"> </span>1<span class="ff5 ls23 wsf">.</span>152.</span></div><div class="t m0 x0 h2 yb6 ff2 fs1 fc0 sc0 lsc2 ws160">d) T<span class="_b blank"></span>udo se passa como se CAP fosse uma<span class="_20 blank"> </span>´<span class="_3 blank"></span><span class="ls28 ws161">unica<span class="_d blank"> </span>letra.<span class="_28 blank"> </span>D ev<span class="_2c blank"></span>emos,<span class="_d blank"> </span>p or-</span></div><div class="t m0 x0 h2 yb7 ff2 fs1 fc0 sc0 ls32 ws162">tan<span class="_2c blank"></span>to,<span class="_6 blank"> </span>arrumar<span class="_8 blank"> </span>em<span class="_6 blank"> </span>\ufb01la<span class="_6 blank"> </span>6<span class="_6 blank"> </span>o<span class="_4 blank"> </span>b jetos:<span class="_f blank"> </span>CAP<span class="_b blank"></span>,I,T,U,L,O.</div><div class="t m0 x0 h2 yb8 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls3 wsf8">e 6!<span class="_f blank"> </span>= 720.</span></div><div class="t m0 x0 h2 yb9 ff2 fs1 fc0 sc0 ls41 ws163">e) Primeiramen<span class="_2c blank"></span>te,<span class="_8 blank"> </span>devemos escolher a<span class="_8 blank"> </span>ordem em que as letras C, A, P</div><div class="t m0 x0 h2 yba ff2 fs1 fc0 sc0 ls57 ws164">aparecer\u02dc<span class="_10 blank"></span><span class="ls74 ws165">ao. H´<span class="_17 blank"></span><span class="ls8 ws166">a 3!<span class="_f blank"> </span>mo<span class="_4 blank"> </span>dos.<span class="_f blank"> </span>Dep<span class="_4 blank"> </span>ois, dev<span class="_2c blank"></span>emos<span class="_8 blank"> </span>arrumar em \ufb01la 6 ob<span class="_1f blank"> </span>jetos:</span></span></div><div class="t m0 x0 h2 ybb ff2 fs1 fc0 sc0 lsc3 ws167">ob<span class="_19 blank"></span>l<span class="_9 blank"></span>o<span class="_1b blank"></span>c<span class="_9 blank"></span>od<span class="_19 blank"></span>a<span class="_9 blank"></span>sl<span class="_9 blank"></span>e<span class="_19 blank"></span>t<span class="_9 blank"></span>r<span class="_9 blank"></span>a<span class="_19 blank"></span>sC<span class="_9 blank"></span>,A<span class="_9 blank"></span>,Pea<span class="_9 blank"></span>s5l<span class="_19 blank"></span>e<span class="_9 blank"></span>t<span class="_19 blank"></span>r<span class="_9 blank"></span>a<span class="_9 blank"></span>sI<span class="_9 blank"></span>,T<span class="_19 blank"></span>,U<span class="_9 blank"></span>,L<span class="_9 blank"></span>,O<span class="_19 blank"></span>.H<span class="_9 blank"></span>´<span class="_1c blank"></span><span class="lsa6 ws168">a6<span class="_9 blank"></span>! m<span class="_9 blank"></span>o<span class="_1b blank"></span>d<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_19 blank"></span>.</span></div><div class="t m0 x0 h2 ybc ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls1f wsa">e3<span class="_9 blank"></span>!<span class="_b blank"></span><span class="ff3 ls0">×<span class="ff2 ls3 ws169">6!<span class="_1e blank"> </span>=<span class="_1e blank"> </span>6 </span>×<span class="ff2 ls3 ws5d">720 = 4320.</span></span></span></div><div class="t m0 x0 h2 ybd ff2 fs1 fc0 sc0 ls40 ws3b">f<span class="_1f blank"> </span>) Basta arrumar<span class="_8 blank"> </span>em \ufb01la, dep<span class="_4 blank"> </span>ois do P<span class="_b blank"></span>A,<span class="_8 blank"> </span>as restan<span class="_2c blank"></span>tes<span class="_8 blank"> </span>6 letras.</div><div class="t m0 x0 h2 ybe ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls3 wsf8">e 6!<span class="_f blank"> </span>= 720.</span></div><div class="t m0 x0 h2 ybf ff2 fs1 fc0 sc0 ls3b ws16a">g) H´<span class="_17 blank"></span><span class="ls34 ws16b">a 7!<span class="_20 blank"> </span>anagramas com a letra P em primeiro l<span class="_7 blank"></span>ugar e h´<span class="_3 blank"></span><span class="lsb9 ws16c">a 7!<span class="_f blank"> </span>anagramas</span></span></div><div class="t m0 x0 h2 yc0 ff2 fs1 fc0 sc0 ls2f ws11f">com a letra A em segundo<span class="_f blank"> </span>lugar.<span class="_34 blank"> </span>H´<span class="_3 blank"></span><span class="ls89 wse7">at<span class="_1a blank"></span>a<span class="_14 blank"></span>m<span class="_11 blank"></span>b<span class="_11 blank"></span>´<span class="_18 blank"></span><span class="ls44 ws16d">em<span class="_f blank"> </span>6!<span class="_34 blank"> </span>anagram<span class="_7 blank"></span>as com P</span></span></div><div class="t m0 x0 h2 yc1 ff2 fs1 fc0 sc0 ls2f ws16e">em primeiro lugar e A em segundo lugar.<span class="_34 blank"> </span>Ao somarmos 7!<span class="_34 blank"> </span>com 7!,</div><div class="t m0 x5 h2 yc2 ff2 fs1 fc0 sc0 ls23">6</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><div class="t m0 x0 h2 y0 ff2 fs1 fc0 sc0 ls2a ws10f">encon<span class="_7 blank"></span>tramos<span class="_d blank"> </span>o<span class="_20 blank"> </span>n ´<span class="_3 blank"></span><span class="ls14 ws16f">umero de anagramas com P em prime<span class="_7 blank"></span>iro lugar ou A</span></div><div class="t m0 x0 h2 y42 ff2 fs1 fc0 sc0 ls70 ws170">em segundo<span class="_d blank"> </span>lugar, mas contamos duas vezes os ana<span class="_4 blank"> </span>gramas que t\u02c6<span class="_10 blank"></span><span class="ls50 ws171">em P</span></div><div class="t m0 x0 h2 y80 ff2 fs1 fc0 sc0 ls37 ws172">em primeiro lugar e A em segundo<span class="_d blank"> </span>lugar.<span class="_2a blank"> </span>A resp<span class="_1f blank"> </span>osta<span class="_6 blank"> </span>´<span class="_11 blank"></span><span class="lsca ws173">e7<span class="_19 blank"></span>!<span class="_2 blank"></span>+<span class="_2f blank"></span>7<span class="_19 blank"></span>!<span class="_b blank"></span><span class="ff3 ls46">\u2212<span class="ff2 ls3 ws174">6! =</span></span></span></div><div class="t m0 x0 h2 y81 ff2 fs1 fc0 sc0 ls3 ws175">5040 + 5040 <span class="ff3 ls0">\u2212</span><span class="ws5d">720 = 9<span class="ff5 ls23 wsf">.</span>360.</span></div><div class="t m0 x0 h2 yc3 ff2 fs1 fc0 sc0 ls52 ws176">h) H´<span class="_17 blank"></span><span class="ls74 ws177">a 7!<span class="_21 blank"> </span>anagramas com a letra P em prime<span class="_7 blank"></span>iro lugar,<span class="_20 blank"> </span>7!<span class="_21 blank"> </span>anagramas</span></div><div class="t m0 x0 h2 yc4 ff2 fs1 fc0 sc0 ls32 ws178">com a<span class="_6 blank"> </span>letra A em segundo e 7!<span class="_32 blank"> </span>anagramas<span class="_6 blank"> </span>com a letra C em terceiro.</div><div class="t m0 x0 h2 yc5 ff2 fs1 fc0 sc0 ls3c ws95">H´<span class="_17 blank"></span><span class="lscb ws179">at<span class="_19 blank"></span>a<span class="_1a blank"></span>m<span class="_1a blank"></span>b<span class="_14 blank"></span>´<span class="_1c blank"></span><span class="ls76 ws123">em<span class="_d blank"> </span>6!<span class="_21 blank"> </span>anagramas com P em primeiro lugar e A em segundo</span></span></div><div class="t m0 x0 h2 yc6 ff2 fs1 fc0 sc0 ls74 ws17a">lugar, 6!<span class="_20 blank"> </span>anagramas com P em prime<span class="_7 blank"></span>iro e C em terceiro e 6!<span class="_d blank"> </span>a<span class="_4 blank"> </span>nagramas</div><div class="t m0 x0 h2 yc7 ff2 fs1 fc0 sc0 lscc wsf4">com A em segundo e C em terceiro.<span class="_f blank"> </span>Finalmente, h´<span class="_10 blank"></span><span class="lsb9 ws17b">a 5!<span class="_f blank"> </span>anagramas com</span></div><div class="t m0 x0 h2 yc8 ff2 fs1 fc0 sc0 ls41 ws17c">P em primeiro lugar, A em segundo e C em terceiro.</div><div class="t m0 x0 h2 yc9 ff2 fs1 fc0 sc0 ls74 ws17d">Ao somarmos 7!<span class="_f blank"> </span>com 7!<span class="_e blank"> </span>com 7!, encon<span class="_2c blank"></span>tramos o n<span class="_4 blank"> </span>´<span class="_3 blank"></span><span class="ls34 wsf6">umero de anagramas</span></div><div class="t m0 x0 h2 yca ff2 fs1 fc0 sc0 ls51 ws103">que t<span class="_7 blank"></span>\u02c6<span class="_11 blank"></span><span class="ls1b ws17e">em P em primeiro lugar ou A em segundo ou C em terceiro,<span class="_8 blank"> </span>mas</span></div><div class="t m0 x0 h2 ycb ff2 fs1 fc0 sc0 ls60 ws17f">con<span class="_2c blank"></span>tamos alguns anagramas v´<span class="_3 blank"></span><span class="ls70 ws180">ar<span class="_4 blank"> </span>ias v<span class="_2c blank"></span>ezes.</span></div><div class="t m0 x0 h2 ycc ff2 fs1 fc0 sc0 ls4e ws181">Con<span class="_7 blank"></span>tamos dua<span class="_4 blank"> </span>s v<span class="_2c blank"></span>ezes<span class="_1d blank"> </span>o<span class="_4 blank"> </span>s anagr<span class="_4 blank"> </span>amas que t\u02c6<span class="_10 blank"></span><span class="ls3e ws182">em P em<span class="_1d blank"> </span>primeiro lug<span class="_4 blank"> </span>ar e A em</span></div><div class="t m0 x0 h2 ycd ff2 fs1 fc0 sc0 ls3e ws183">segundo;<span class="_1e blank"> </span>o mesmo<span class="_1e blank"> </span>se deu com os que<span class="_1d blank"> </span>t\u02c6<span class="_10 blank"></span><span class="ls1c ws184">em P em primeiro e C em terceiro</span></div><div class="t m0 x0 h2 yce ff2 fs1 fc0 sc0 ls3 ws185">e com os que t<span class="_7 blank"></span>\u02c6<span class="_10 blank"></span><span class="ls3a ws186">em A em segundo e C em tercei<span class="ls2d ws187">ro.<span class="_16 blank"> </span>Descontando essas</span></span></div><div class="t m0 x0 h2 ycf ff2 fs1 fc0 sc0 ls5f ws188">con<span class="_2c blank"></span>tagens indevidas, c<span class="_2c blank"></span>hegamos a 7!<span class="_38 blank"> </span>+<span class="_38 blank"> </span>7!<span class="_38 blank"> </span>+<span class="_38 blank"> </span>7!<span class="_38 blank"> </span><span class="ff3 ls78">\u2212</span><span class="ls3 ws189">6! <span class="ff3 ls78">\u2212</span>6! <span class="ff3 ls78">\u2212</span><span class="ws5d">6! = 3<span class="ff5 ls23 wsf">.</span></span>7! <span class="ff3 ls78">\u2212</span><span class="ls44">3<span class="ff5 ls23 wsf">.</span></span></span>6!.</div><div class="t m0 x0 h2 yd0 ff2 fs1 fc0 sc0 ls2f ws18a">En<span class="_2c blank"></span>tretanto, anagramas com P<span class="_6 blank"> </span>em primeiro lugar e A em segundo e C</div><div class="t m0 x0 h2 yd1 ff2 fs1 fc0 sc0 ls56 ws18b">em terceiro foram, inicialmente, contados tr<span class="_2c blank"></span>\u02c6<span class="_11 blank"></span><span class="ls39 ws18c">es<span class="_6 blank"> </span>v<span class="_2c blank"></span>ezes<span class="_8 blank"> </span>e,<span class="_6 blank"> </span>p o steriormen<span class="_2c blank"></span>te,</span></div><div class="t m0 x0 h2 yd2 ff2 fs1 fc0 sc0 ls2f ws18d">descon<span class="_2c blank"></span>tados tr\u02c6<span class="_10 blank"></span><span class="ls2c ws70">es vezes, o que sig<span class="_4 blank"> </span>ni\ufb01ca que<span class="_20 blank"> </span>n\u02dc<span class="_10 blank"></span><span class="ls87 ws18e">ao est\u02dc<span class="_3 blank"></span><span class="ls8 ws18f">ao sendo contados.</span></span></span></div><div class="t m0 x0 h2 yd3 ff2 fs1 fc0 sc0 lsa7 ws190">Incluindo-os na con<span class="_2c blank"></span>tagem,<span class="_20 blank"> </span>obtemos a resposta correta, que ´<span class="_10 blank"></span><span class="ls77 wsab">e3<span class="_19 blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls61 wse0">(7!) </span><span class="ff3">\u2212</span></span></span></div><div class="t m0 x0 h2 yd4 ff2 fs1 fc0 sc0 ls44">3<span class="ff5 ls23 wsf">.</span><span class="ls61 ws191">(6!) + 5!<span class="_1e blank"> </span>=<span class="_1e blank"> </span>3</span><span class="ff5 ls23 wsf">.</span><span class="ls14 ws4a">(5</span><span class="ff5 ls23 wsf">.</span><span class="ls3 ws192">040) <span class="ff3 ls11">\u2212</span></span>3<span class="ff5 ls23 wsf">.</span><span class="ls9 ws193">(720) +<span class="_1d blank"> </span>120<span class="_1d blank"> </span>=<span class="_1e blank"> </span>13</span><span class="ff5 ls23 wsf">.</span><span class="ls3">080.</span></div><div class="t m0 x0 h2 yd5 ff2 fs1 fc0 sc0 lscc ws194">i) Como h´<span class="_17 blank"></span><span class="ls53 ws52">a<span class="_d blank"> </span>6<span class="_d blank"> </span>ordens<span class="_d blank"> </span>p o ss<span class="_2 blank"></span>´<span class="_19 blank"></span><span class="ls60 ws195">\u0131v<span class="_2c blank"></span>eis<span class="_20 blank"> </span>para as letras C, A e P<span class="_b blank"></span>,<span class="_d blank"> </span>o<span class="_4 blank"> </span>s anagramas</span></span></div><div class="t m0 x0 h2 yd6 ff2 fs1 fc0 sc0 ls76 ws11e">p edidos<span class="_6 blank"> </span>s\u02dc<span class="_17 blank"></span><span class="ls6d wsa7">ao exatamen<span class="_2c blank"></span>te<span class="_8 blank"> </span>1/6 do total, ou seja, 8!<span class="ff5 ls44">/</span><span class="ls55 ws54">6=6<span class="_c blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3">720.</span></span></span></span></div><div class="t m0 x0 h2 yd7 ff1 fs1 fc0 sc0 ls2a ws18">Outra solu¸<span class="_17 blank"></span><span class="ls2b ws19">c\u02dc<span class="_3 blank"></span><span class="ls2c">ao:</span></span></div><div class="t m0 x0 h2 yd8 ff2 fs1 fc0 sc0 ls5a ws196">Basta escolher<span class="_d blank"> </span>as 3 po<span class="_4 blank"> </span>si¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_17 blank"></span><span class="ls56 ws197">oes<span class="_8 blank"> </span>a serem<span class="_8 blank"> </span>o<span class="_1f blank"> </span>cupadas pelas Letras P<span class="_39 blank"></span>, A, C, o</span></span></div><div class="t m0 x0 h13 yd9 ff2 fs1 fc0 sc0 ls2c ws130">que<span class="_8 blank"> </span>p o de<span class="_8 blank"> </span>ser<span class="_d blank"> </span>feito<span class="_8 blank"> </span>de<span class="_8 blank"> </span><span class="ff5 lsc4">C<span class="ff4 fs2 ls23 v3">3</span></span></div><div class="t m0 x13 h14 yda ff4 fs2 fc0 sc0 lsc5">8<span class="ff2 fs1 ls76 ws198 v4">=<span class="_6 blank"> </span>56 mo<span class="_4 blank"> </span>dos e distribuir as 5<span class="_6 blank"> </span>letras restantes</span></div><div class="t m0 x0 h2 ydb ff2 fs1 fc0 sc0 ls3b ws33">nas<span class="_8 blank"> </span>demais<span class="_8 blank"> </span>p osi¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_17 blank"></span><span class="ls14 ws199">oes,<span class="_d blank"> </span>o<span class="_8 blank"> </span>que<span class="_8 blank"> </span>p o de<span class="_8 blank"> </span>ser<span class="_8 blank"> </span>feito<span class="_8 blank"> </span>de<span class="_8 blank"> </span>5!<span class="_6 blank"> </span>=<span class="_6 blank"> </span>120<span class="_8 blank"> </span>mo dos.<span class="_32 blank"> </span>O<span class="_8 blank"> </span>total</span></span></div><div class="t m0 x0 h2 ydc ff2 fs1 fc0 sc0 ls26 ws19a">de<span class="_6 blank"> </span>anagramas ´<span class="_10 blank"></span><span class="ls38 ws2d">e5<span class="_9 blank"></span>6<span class="_b blank"></span><span class="ff3 ls11">×<span class="ff2 ls3 ws2e">120 = 6<span class="ff5 ls23 wsf">.</span>720.</span></span></span></div><div class="t m0 x1 h2 ydd ff1 fs1 fc0 sc0 ls1b ws6">2) <span class="ff2 ls5 ws185">O v<span class="_39 blank"></span>alor<span class="_d blank"> </span>de <span class="ff5 lsc6">f</span><span class="ls8">(<span class="ff5 ls23 wsf">a<span class="ff4 fs2 ls49 v2">1</span></span><span class="ls70 ws19b v0">) p<span class="_4 blank"> </span>o<span class="_1f blank"> </span>de ser escolhido de n mo<span class="_4 blank"> </span>do<span class="_4 blank"> </span>s; o v<span class="_2c blank"></span>alor de <span class="ff5 lsc6">f</span><span class="ls8">(<span class="ff5 ls23 wsf">a<span class="ff4 fs2 ls49 v2">2</span></span><span class="ls76 ws19c">), de</span></span></span></span></span></div><div class="t m0 x0 h2 yde ff5 fs1 fc0 sc0 lsc7">n<span class="ff3 ls0">\u2212<span class="ff2 lsa6 ws19d">1m<span class="_9 blank"></span>o<span class="_1b blank"></span>d<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_19 blank"></span>;<span class="ff5 ls64 ws8c">...</span><span class="lsa8 ws136">;od<span class="_19 blank"></span>e<span class="ff5 lsc6">f</span><span class="ls8">(<span class="ff5 ls23 wsf">a<span class="ff6 fs2 ls4 v2">n</span></span><span class="ls5 ws19e v0">),<span class="_6 blank"> </span>de<span class="_6 blank"> </span>1<span class="_8 blank"> </span>mo do.</span></span></span></span></span></div><div class="t m0 x0 h2 ydf ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="lsc8">e<span class="ff5 ls23 wsf">n</span><span class="ls8">(<span class="ff5 lsc9">n<span class="ff3 ls11">\u2212</span></span><span class="ls3 ws19f">1) <span class="ff5 ls64 ws8c">...</span><span class="ls55 ws54">1=<span class="ff5 ls23 wsf">n<span class="ff2">!</span></span></span></span></span></span></div><div class="t m0 x1 h2 y7d ff1 fs1 fc0 sc0 ls1b ws6">3) <span class="ff2 ls22 wse">On<span class="_24 blank"></span>´<span class="_2e blank"></span><span class="ls5f ws1a0">umero total de mo<span class="_4 blank"> </span>dos de sen<span class="_2c blank"></span>tar<span class="_1e blank"> </span>8 p<span class="_4 blank"> </span>essoas em 8 cadeiras ´<span class="_17 blank"></span><span class="lscd ws1a1">eo<span class="_4 blank"> </span>n<span class="_24 blank"></span>´<span class="_a blank"></span><span class="ls53">umero</span></span></span></span></div><div class="t m0 x0 h2 y7e ff2 fs1 fc0 sc0 ls5 wsd7">de<span class="_20 blank"> </span>mo dos<span class="_20 blank"> </span>de<span class="_f blank"> </span>arrumar<span class="_20 blank"> </span>8<span class="_20 blank"> </span>p essoas<span class="_20 blank"> </span>em<span class="_f blank"> </span>\ufb01la,<span class="_20 blank"> </span>8!.<span class="_34 blank"> </span>O<span class="_20 blank"> </span>n ´<span class="_3 blank"></span><span class="ls24 ws6f">umero<span class="_f blank"> </span>de<span class="_20 blank"> </span>mo dos<span class="_20 blank"> </span>de</span></div><div class="t m0 x5 h2 y7f ff2 fs1 fc0 sc0 ls23">7</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x14 ye0 w1 h15" alt="" src="https://files.passeidireto.com/58b4a18f-e503-45f3-8943-ef24d4471d15/bg8.png"><div class="t m0 x0 h2 y0 ff2 fs1 fc0 sc0 ls41 ws1a2">arrumar 8 p<span class="_4 blank"> </span>essoas em \ufb01la de<span class="_e blank"> </span>mo<span class="_4 blank"> </span>do que duas dessas p<span class="_4 blank"> </span>essoas,<span class="_32 blank"> </span>V<span class="_b blank"></span>era e</div><div class="t m0 x0 h2 y42 ff2 fs1 fc0 sc0 ls29 ws1a3">P<span class="_2c blank"></span>aulo,<span class="_e blank"> </span>\ufb01quem<span class="_f blank"> </span>jun<span class="_2c blank"></span>tas ´<span class="_11 blank"></span><span class="ls32 ws1a4">e<span class="_20 blank"> </span>2.7!, p<span class="_4 blank"> </span>ois,<span class="_e blank"> </span>para<span class="_20 blank"> </span>formar uma<span class="_20 blank"> </span>tal \ufb01la, dev<span class="_2c blank"></span>emos</span></div><div class="t m0 x0 h2 y80 ff2 fs1 fc0 sc0 ls3f ws11a">inicialmen<span class="_2c blank"></span>te<span class="_e blank"> </span>decidir<span class="_e blank"> </span>em que ordem se colo<span class="_4 blank"> </span>car\u02dc<span class="_17 blank"></span><span class="ls3b ws1a5">ao V<span class="_39 blank"></span>era e P<span class="_2c blank"></span>aulo e,<span class="_32 blank"> </span>em</span></div><div class="t m0 x0 h2 y81 ff2 fs1 fc0 sc0 ls82 ws1a6">seguida,<span class="_e blank"> </span>formar uma \ufb01la de 7 ob<span class="_1f blank"> </span>jetos:<span class="_26 blank"> </span>o blo<span class="_4 blank"> </span>co formado p<span class="_4 blank"> </span>or V<span class="_39 blank"></span>era e</div><div class="t m0 x0 h2 y61 ff2 fs1 fc0 sc0 ls3b ws1a7">P<span class="_2c blank"></span>aulo; as demais 6<span class="_8 blank"> </span>p<span class="_4 blank"> </span>essoas.</div><div class="t m0 x0 h2 ye1 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="ls72 ws1a8">e 8!<span class="_f blank"> </span>- 2.7!<span class="_f blank"> </span>= 40.320 - 10.080 = 30.240.</span></div><div class="t m0 x1 h2 ye2 ff1 fs1 fc0 sc0 ls1b ws6">4) <span class="ff2 lsdc ws1a9">C<span class="_10 blank"></span>o<span class="_11 blank"></span>m<span class="_11 blank"></span>ov<span class="_10 blank"></span>i<span class="_11 blank"></span>s<span class="_10 blank"></span>t<span class="_11 blank"></span>on<span class="_10 blank"></span>op<span class="_11 blank"></span>r<span class="_11 blank"></span>o<span class="_10 blank"></span>b<span class="_11 blank"></span>l<span class="_11 blank"></span>e<span class="_10 blank"></span>m<span class="_11 blank"></span>a<span class="_7 blank"></span>a<span class="_11 blank"></span>n<span class="_17 blank"></span>t<span class="_11 blank"></span>e<span class="_10 blank"></span>r<span class="_11 blank"></span>i<span class="_11 blank"></span>o<span class="_10 blank"></span>r<span class="_11 blank"></span>, on<span class="_11 blank"></span>´<span class="_3a blank"></span><span class="ls2f wsc5">umero de \ufb01las nas quais duas</span></span></div><div class="t m0 x0 h2 ye3 ff2 fs1 fc0 sc0 ls3e ws1aa">p<span class="_4 blank"> </span>essoas (neste caso<span class="_20 blank"> </span>Helena<span class="_f blank"> </span>e P<span class="_2c blank"></span>edro) \ufb01cam juntas<span class="_8 blank"> </span>´<span class="_11 blank"></span><span class="lsdd ws1ab">e2<span class="_1a blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3 ws1ac">7! = 10</span>.<span class="ff2 ls3 ws1ad">080. O</span></span></span></div><div class="t m0 x0 h2 ye4 ff2 fs1 fc0 sc0 ls71 ws7b">n´<span class="_15 blank"></span><span class="ls37 ws1ae">umero<span class="_e blank"> </span>de \ufb01las onde Helena<span class="_e blank"> </span>e P<span class="_2c blank"></span>edro<span class="_e blank"> </span>e tamb<span class="_2c blank"></span>´<span class="_10 blank"></span><span class="ls23 ws1af">em<span class="_e blank"> </span>V<span class="_b blank"></span>era e Paulo \ufb01cam</span></span></div><div class="t m0 x0 h2 ye5 ff2 fs1 fc0 sc0 ls60 ws1b0">jun<span class="_2c blank"></span>tos ´<span class="_11 blank"></span><span class="lsde ws1b1">eo<span class="_1a blank"></span>b<span class="_19 blank"></span>t<span class="_1a blank"></span>i<span class="_19 blank"></span>d<span class="_14 blank"></span>o<span class="_4 blank"> </span>d<span class="_1a blank"></span>em<span class="_19 blank"></span>o<span class="_19 blank"></span>d<span class="_1a blank"></span>oa<span class="_19 blank"></span>n<span class="_1a blank"></span>´<span class="_37 blank"></span><span class="ls44 ws1b2">alogo:<span class="_2a blank"> </span>agora s\u02dc<span class="_17 blank"></span><span class="ls2f ws19b">ao dois blo<span class="_4 blank"> </span>cos de duas p<span class="_1f blank"> </span>es-</span></span></span></div><div class="t m0 x0 h2 ye6 ff2 fs1 fc0 sc0 ls3f ws1b3">soas, cada um p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>dendo ser arrumado de dois mo<span class="_4 blank"> </span>dos distin<span class="_2c blank"></span>t<span class="_4 blank"> </span>os e mais</div><div class="t m0 x0 h2 ye7 ff2 fs1 fc0 sc0 ls92 ws1b4">4<span class="_d blank"> </span>pessoas.<span class="_27 blank"> </span>P<span class="_7 blank"></span>ortan<span class="_2c blank"></span>to,<span class="_20 blank"> </span>o<span class="_d blank"> </span>n ´<span class="_3 blank"></span><span class="ls76 ws1b5">umero<span class="_d blank"> </span>de<span class="_d blank"> </span>tais<span class="_d blank"> </span>\ufb01las ´<span class="_11 blank"></span><span class="lsdf ws1b6">e2<span class="_1a blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls44">2</span>.<span class="ff2 ls3 ws85">6! = 2</span>.<span class="ff2 ls9 ws1b7">880.<span class="_27 blank"> </span>Logo, o</span></span></span></span></div><div class="t m0 x0 h2 ye8 ff2 fs1 fc0 sc0 ls71 ws7b">n´<span class="_15 blank"></span><span class="ls56 ws1b8">umero de<span class="_25 blank"> </span>\ufb01las em que<span class="_6 blank"> </span>Helena e Pedro \ufb01cam juntos, mas V<span class="_b blank"></span>era e Paulo</span></div><div class="t m0 x0 h2 ye9 ff2 fs1 fc0 sc0 ls53 wsb4">n\u02dc<span class="_17 blank"></span><span class="ls3 ws9b">ao, ´<span class="_11 blank"></span><span class="ls38 ws2d">e1<span class="_19 blank"></span>0<span class="_9 blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3 wsa8">080 <span class="ff3 ls0">\u2212</span><span class="ls44">2</span></span>.<span class="ff2 ls3 wsa9">880 =<span class="_1e blank"> </span>7</span>.<span class="ff2 ls3 ws10">200</span>.</span></span></span></div><div class="t m0 x1 h2 yea ff1 fs1 fc0 sc0 ls1b ws6">5) <span class="ff2 ls22 ws1b9">Oe<span class="_1b blank"></span>l<span class="_c blank"></span>e<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_9 blank"></span>t<span class="_c blank"></span>o<span class="_4 blank"> </span>d<span class="_c blank"></span>a p<span class="_24 blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>m<span class="_1b blank"></span>u<span class="_1b blank"></span>t<span class="_c blank"></span>a<span class="_c blank"></span>¸<span class="_1 blank"></span><span class="ls50 ws47">c\u02dc<span class="_17 blank"></span><span class="ls55 ws1ba">a<span class="_c blank"></span>oq<span class="_c blank"></span>u<span class="_c blank"></span>eo<span class="_22 blank"></span>c<span class="_1b blank"></span>u<span class="_c blank"></span>p<span class="_c blank"></span>ao1<span class="_c blank"></span>0</span></span></span></div><div class="t m0 x15 h3 yeb ff4 fs2 fc0 sc0 ls13">o<span class="ff2 fs1 ls3b ws1bb v1">lugar dev<span class="_2c blank"></span>e<span class="_1e blank"> </span>ser<span class="_25 blank"> </span>maior que 7.</span></div><div class="t m0 x0 hb yec ff2 fs1 fc0 sc0 ls28 ws1bc">P<span class="_2c blank"></span>o de<span class="_1d blank"> </span>ser<span class="_1d blank"> </span>escolhido<span class="_1d blank"> </span>de<span class="_1d blank"> </span>3<span class="_23 blank"> </span>mo dos.<span class="_f blank"> </span>O<span class="_1d blank"> </span>elemen<span class="_2c blank"></span>to<span class="_1d blank"> </span>da<span class="_1d blank"> </span>9<span class="ff4 fs2 ls45 v3">a</span><span class="ls71 ws7b v0">po<span class="_2c blank"></span>si<span class="_2c blank"></span>¸<span class="_10 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls34 ws1bd">ao dev<span class="_7 blank"></span>e ser maior</span></span></span></div><div class="t m0 x0 h2 yed ff2 fs1 fc0 sc0 ls3f ws1be">que 6; hav<span class="_39 blank"></span>eria<span class="_d blank"> </span>4 possibilidades,<span class="_d blank"> </span>mas uma delas j´<span class="_3 blank"></span><span class="ls40 ws1bf">a foi usada na escolha</span></div><div class="t m0 x0 h16 yee ff2 fs1 fc0 sc0 ls2e ws1c0">do elemen<span class="_2c blank"></span>to<span class="_d blank"> </span>que o<span class="_4 blank"> </span>cupa a 10<span class="ff4 fs2 lsce v3">a</span><span class="ls71 ws7b v0">pos<span class="_2c blank"></span>i<span class="_7 blank"></span>¸<span class="_10 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls41 ws1c1">ao.<span class="_32 blank"> </span>P<span class="_2c blank"></span>o de<span class="_8 blank"> </span>ser<span class="_8 blank"> </span>escolhido<span class="_d blank"> </span>de<span class="_6 blank"> </span>3<span class="_8 blank"> </span>mo dos.</span></span></span></div><div class="t m0 x0 h2 yef ff2 fs1 fc0 sc0 lsc2 ws1c2">Prosseguindo<span class="_1e blank"> </span>com<span class="_1e blank"> </span>esse<span class="_1d blank"> </span>ra cio c<span class="_2f blank"></span>´<span class="_1a blank"></span><span class="ls3f ws1c3">\u0131nio,<span class="_1e blank"> </span>v<span class="_7 blank"></span>emos que a cada<span class="_1e blank"> </span>no<span class="_2c blank"></span>v<span class="_2c blank"></span>a casa abranda-</span></div><div class="t m0 x0 h2 yf0 ff2 fs1 fc0 sc0 ls41 ws1c4">se a restri¸<span class="_11 blank"></span><span class="ls50 ws47">c\u02dc<span class="_10 blank"></span><span class="ls29 wsbf">ao,<span class="_25 blank"> </span>criando<span class="_25 blank"> </span>uma<span class="_6 blank"> </span>p ossibilidade<span class="_25 blank"> </span>a<span class="_25 blank"> </span>mais,<span class="_6 blank"> </span>mas<span class="_25 blank"> </span>ao<span class="_25 blank"> </span>mesmo<span class="_25 blank"> </span>t emp o</span></span></div><div class="t m0 x0 h2 yf1 ff2 fs1 fc0 sc0 ls37 ws116">dimin<span class="_2c blank"></span>ui-<span class="_4 blank"> </span>se uma p<span class="_4 blank"> </span>ossibilidade,<span class="_20 blank"> </span>p<span class="_4 blank"> </span>ois uma delas foi usada na etapa.<span class="_16 blank"> </span>Ou</div><div class="t m0 x0 h2 yf2 ff2 fs1 fc0 sc0 lse0 ws1c5">seja, h´<span class="_10 blank"></span><span class="ls3c ws1c6">a 3 p<span class="_4 blank"> </span>ossibilidades para cada casa at<span class="_2c blank"></span>´<span class="_11 blank"></span><span class="lscf ws1c7">ea3</span></span></div><div class="t m0 x16 h3 yf3 ff4 fs2 fc0 sc0 lsd0">a<span class="ff2 fs1 ls2c wsda v1">casa.<span class="_28 blank"> </span>O elemento da</span></div><div class="t m0 x0 hb yf4 ff2 fs1 fc0 sc0 lsd1">3<span class="ff4 fs2 lsd2 v3">a</span><span class="ls71 ws7b v0">po<span class="_7 blank"></span>s<span class="_2c blank"></span>i¸<span class="_10 blank"></span><span class="ls50 ws47">c\u02dc<span class="_17 blank"></span><span class="ls34 ws1c8">ao dev<span class="_7 blank"></span>e ser maior<span class="_20 blank"> </span>que 3<span class="_25 blank"> </span><span class="ff3 ls4d">\u2212</span><span class="ls37 ws1c9">3<span class="_e blank"> </span>=<span class="_e blank"> </span>0;<span class="_32 blank"> </span>ha<span class="_7 blank"></span>v<span class="_2c blank"></span>eria<span class="_e blank"> </span>10<span class="_f blank"> </span>p ossibilidades,</span></span></span></span></div><div class="t m0 x0 h2 yf5 ff2 fs1 fc0 sc0 ls3e ws1ca">mas 7 delas<span class="_8 blank"> </span>j´<span class="_10 blank"></span><span class="ls24 ws1cb">a foram usadas nas etapas an<span class="_7 blank"></span>teriores.<span class="_e blank"> </span>Pode<span class="_8 blank"> </span>ser<span class="_8 blank"> </span>escolhido</span></div><div class="t m0 x0 h16 yf6 ff2 fs1 fc0 sc0 ls61 ws1cc">de<span class="_d blank"> </span>10 <span class="ff3 ls65">\u2212</span><span class="ls28 ws18d">7 = 3 mo<span class="_4 blank"> </span>dos.<span class="_26 blank"> </span>O elemen<span class="_39 blank"></span>to<span class="_f blank"> </span>da 2<span class="ff4 fs2 lsd3 v3">a</span><span class="ls71 ws7b v0">po<span class="_7 blank"></span>s<span class="_2c blank"></span>i¸<span class="_10 blank"></span><span class="ls50 ws47">c\u02dc<span class="_17 blank"></span><span class="ls34 ws1cd">ao dev<span class="_2c blank"></span>e<span class="_f blank"> </span>ser m<span class="_7 blank"></span>aior que</span></span></span></span></div><div class="t m0 x0 h2 yf7 ff2 fs1 fc0 sc0 lsd4">2<span class="ff3 lsd5">\u2212</span><span class="ls2 wsc">3=</span><span class="ff3 ls23 ws4f">\u2212</span><span class="ls32 ws1ce">1; ha<span class="_2c blank"></span>veria 10 possibilidades,<span class="_8 blank"> </span>mas 8 delas j´<span class="_3 blank"></span><span class="ls5f ws1cf">a<span class="_6 blank"> </span>foram usadas nas</span></span></div><div class="t m0 x0 h2 yf8 ff2 fs1 fc0 sc0 ls2e ws1d0">etapas<span class="_1d blank"> </span>a n<span class="_2c blank"></span>teriores.<span class="_f blank"> </span>P<span class="_7 blank"></span>o de<span class="_1e blank"> </span>ser<span class="_1d blank"> </span>escolhido<span class="_1e blank"> </span>de<span class="_1e blank"> </span>10<span class="_3b blank"> </span><span class="ff3 lsd6">\u2212</span><span class="ls3b ws7">8<span class="_1e blank"> </span>=<span class="_1d blank"> </span>2<span class="_1e blank"> </span>mo dos.<span class="_d blank"> </span>F inalmen<span class="_39 blank"></span>te,</span></div><div class="t m0 x0 h2 yf9 ff2 fs1 fc0 sc0 ls53 ws52">o<span class="_20 blank"> </span>elemento<span class="_20 blank"> </span>de<span class="_20 blank"> </span>p osi¸<span class="_14 blank"></span><span class="ls50 ws47">c\u02dc<span class="_17 blank"></span><span class="ls57 ws1d1">a<span class="_4 blank"> </span>o<span class="_f blank"> </span>1<span class="_20 blank"> </span>dev<span class="_2c blank"></span>e<span class="_f blank"> </span>ser<span class="_f blank"> </span>maior<span class="_f blank"> </span>que<span class="_20 blank"> </span>1 <span class="ff3 ls4b">\u2212</span><span class="ls83 wsca">3=<span class="ff3 ls23 ws4f">\u2212<span class="ff2 ws1d2">2;<span class="_e blank"> </span>ha<span class="_7 blank"></span>v<span class="_2c blank"></span>eria 10</span></span></span></span></span></div><div class="t m0 x0 h2 yfa ff2 fs1 fc0 sc0 ls24 ws1d3">p<span class="_4 blank"> </span>ossibilidades,<span class="_25 blank"> </span>mas 9 delas j´<span class="_3 blank"></span><span class="ls3b ws1d4">a foram usadas nas etapas an<span class="_2c blank"></span>teriores.<span class="_20 blank"> </span>P<span class="_7 blank"></span>o<span class="_4 blank"> </span>de</span></div><div class="t m0 x0 h2 yfb ff2 fs1 fc0 sc0 ls1c ws1d5">ser<span class="_6 blank"> </span>escolhido<span class="_8 blank"> </span>de<span class="_6 blank"> </span>10 <span class="ff3 ls11">\u2212</span><span class="ls2 ws6c">9=1 m<span class="_c blank"></span>o<span class="_c blank"></span>d<span class="_c blank"></span>o<span class="_1b blank"></span>.<span class="_38 blank"> </span>A r<span class="_c blank"></span>e<span class="_1b blank"></span>s<span class="_1b blank"></span>p<span class="_24 blank"></span>o<span class="_c blank"></span>s<span class="_1b blank"></span>t<span class="_1b blank"></span>a ´<span class="_30 blank"></span><span class="ls1f">e3</span></span></div><div class="t m0 x17 h3 yfc ff4 fs2 fc0 sc0 lsc">8<span class="ff5 fs1 ls23 wsf v1">.<span class="ff2 ls44">2</span>.<span class="ff2 ls66 ws1d6">1=1<span class="_c blank"></span>3<span class="_c blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3">122.</span></span></span></span></div><div class="t m0 x1 h17 yfd ff1 fs1 fc0 sc0 ls1b ws6">6) <span class="ff2 ls3c ws95">H´<span class="_17 blank"></span><span class="lsd7">a<span class="ff5 lsd8">C<span class="ff4 fs2 ls23 v3">5</span></span></span></span></div><div class="t m0 x18 h18 yfe ff4 fs2 fc0 sc0 ls21 ws1d7">15 <span class="ff2 fs1 ls70 ws57 v4">mo dos<span class="_25 blank"> </span>de<span class="_6 blank"> </span>formar<span class="_6 blank"> </span>o<span class="_1e blank"> </span>Esp o rte;<span class="_25 blank"> </span>dep o is<span class="_25 blank"> </span>disso,<span class="_6 blank"> </span><span class="ff5 lsd9">C</span></span><span class="ls23 v5">5</span></div><div class="t m0 x19 h19 yfe ff4 fs2 fc0 sc0 lse1 ws1d8">10 <span class="ff2 fs1 ls57 ws5a v4">mo dos<span class="_25 blank"> </span>de<span class="_25 blank"> </span>fo rmar</span></div><div class="t m0 x0 h2 yff ff2 fs1 fc0 sc0 ls52 ws1d9">o T<span class="_b blank"></span>upi; \ufb01nalmente, 1<span class="_d blank"> </span>´<span class="_3 blank"></span><span class="ls37 ws8d">unico mo<span class="_4 blank"> </span>do de formar o<span class="_8 blank"> </span>Minas.</span></div><div class="t m0 x0 h1a y100 ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="lsc8">e<span class="ff5 lsda">C<span class="ff4 fs2 ls23 v3">5</span></span></span></div><div class="t m0 x1a h18 y101 ff4 fs2 fc0 sc0 ls21 ws1da">15 <span class="ff3 fs1 ls0 v4">×<span class="ff5 lsdb">C</span></span><span class="ls23 v5">5</span></div><div class="t m0 x1b h19 y101 ff4 fs2 fc0 sc0 ls21 ws1db">10 <span class="ff3 fs1 ls0 v4">×<span class="ff2 ls3 ws2e">1 = 756<span class="ff5 ls23 wsf">.</span>756.</span></span></div><div class="t m0 x1 h2 y102 ff1 fs1 fc0 sc0 ls1b ws6">7) <span class="ff2 lse2 ws1dc">On<span class="_11 blank"></span>´<span class="_3c blank"></span><span class="lscc ws19e">umero<span class="_e blank"> </span>de<span class="_32 blank"> </span>p ossibilidades<span class="_e blank"> </span>´<span class="_11 blank"></span><span class="lsb9 ws1dd">e<span class="_e blank"> </span>igual<span class="_e blank"> </span>ao<span class="_32 blank"> </span>n ´<span class="_3 blank"></span><span class="lsa4 ws1de">u<span class="_17 blank"></span>m<span class="_10 blank"></span>e<span class="_10 blank"></span>r<span class="_10 blank"></span>oo<span class="_17 blank"></span>b<span class="_10 blank"></span>t<span class="_10 blank"></span>i<span class="_10 blank"></span>d<span class="_17 blank"></span>on<span class="_10 blank"></span>op<span class="_10 blank"></span>r<span class="_10 blank"></span>o<span class="_17 blank"></span>b<span class="_10 blank"></span>l<span class="_10 blank"></span>e<span class="_17 blank"></span>m<span class="_10 blank"></span>a</span></span></span></span></div><div class="t m0 x5 h2 y103 ff2 fs1 fc0 sc0 ls23">8</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y104 w2 h1b" alt="" src="https://files.passeidireto.com/58b4a18f-e503-45f3-8943-ef24d4471d15/bg9.png"><div class="t m0 x0 h2 y0 ff2 fs1 fc0 sc0 ls4f ws1df">an<span class="_2c blank"></span>terior dividido<span class="_8 blank"> </span>p<span class="_4 blank"> </span>or 3!<span class="_f blank"> </span>= 6, j´<span class="_17 blank"></span><span class="ls32 ws1e0">a<span class="_6 blank"> </span>que<span class="_6 blank"> </span>p<span class="_1f blank"> </span>erm<span class="_2c blank"></span>utando<span class="_8 blank"> </span>os nomes<span class="_6 blank"> </span>dos times<span class="_8 blank"> </span>a</span></div><div class="t m0 x0 h2 y42 ff2 fs1 fc0 sc0 ls5a ws7a">sub divis\u02dc<span class="_17 blank"></span><span class="ls39 ws1e1">ao<span class="_8 blank"> </span>co<span class="_4 blank"> </span>n<span class="_2c blank"></span>tinua a mesma.<span class="_f blank"> </span>A resp<span class="_4 blank"> </span>osta<span class="_25 blank"> </span>´<span class="_11 blank"></span><span class="ls3 ws34">e 756<span class="ff5 ls23 wsf">.</span><span class="ws10">756<span class="ff5 ls44">/</span><span class="wsa9">6 = 126<span class="ff5 ls23 wsf">.</span></span>126<span class="ff5 ls23">.</span></span></span></span></div><div class="t m0 x1 h2 y22 ff1 fs1 fc0 sc0 ls1b ws6">8) <span class="ff2 ls60 ws1e2">Escolha, suc<span class="_7 blank"></span>essiv<span class="_39 blank"></span>amen<span class="_2c blank"></span>te,<span class="_d blank"> </span>3 p<span class="_1f blank"> </span>ess<span class="_7 blank"></span>oas para formar os<span class="_6 blank"> </span>4 grup<span class="_4 blank"> </span>os de 3; isto</span></div><div class="t m0 x0 h1c y23 ff2 fs1 fc0 sc0 ls2c ws130">p o de<span class="_1d blank"> </span>ser<span class="_25 blank"> </span>feito,<span class="_1e blank"> </span>sucessiv<span class="_2c blank"></span>amente,<span class="_25 blank"> </span>de<span class="_1e blank"> </span><span class="ff5 lse3">C<span class="ff4 fs2 ls23 v3">3</span></span></div><div class="t m0 x1c h18 y105 ff4 fs2 fc0 sc0 ls21 ws1e3">20 <span class="ff2 fs1 lsab v4">,<span class="ff5 lse4">C</span></span><span class="ls23 v5">3</span></div><div class="t m0 x1d h18 y105 ff4 fs2 fc0 sc0 ls21 ws1e4">17 <span class="ff2 fs1 lsab v4">,<span class="ff5 lse4">C</span></span><span class="ls23 v5">3</span></div><div class="t m0 x1e h18 y105 ff4 fs2 fc0 sc0 ls21 ws1e3">14 <span class="ff2 fs1 lse5 v4">e<span class="ff5 lse6">C</span></span><span class="ls23 v5">3</span></div><div class="t m0 x19 h1d y105 ff4 fs2 fc0 sc0 lse1 ws1e5">11 <span class="ff2 fs1 ls2d ws111 v4">mo dos.<span class="_20 blank"> </span>A<span class="_1e blank"> </span>seguir,</span></div><div class="t m0 x0 h2 y106 ff2 fs1 fc0 sc0 ls6d wse6">com<span class="_25 blank"> </span>as<span class="_25 blank"> </span>8<span class="_6 blank"> </span>p essoas<span class="_1e blank"> </span>restan<span class="_7 blank"></span>tes<span class="_6 blank"> </span>forme<span class="_25 blank"> </span>os<span class="_25 blank"> </span>2<span class="_6 blank"> </span>grup os<span class="_25 blank"> </span>restan<span class="_2c blank"></span>tes,<span class="_6 blank"> </span>o<span class="_25 blank"> </span>que<span class="_6 blank"> </span>p o de<span class="_25 blank"> </span>ser</div><div class="t m0 x0 h1e y107 ff2 fs1 fc0 sc0 ls74 ws13d">feito de <span class="ff5 lse7">C<span class="ff4 fs2 ls23 v3">4</span></span></div><div class="t m0 x1f h18 y108 ff4 fs2 fc0 sc0 lse8">8<span class="ff2 fs1 lse9 v4">e<span class="ff5 lsea">C</span></span><span class="ls23 v5">4</span></div><div class="t m0 x1a h19 y108 ff4 fs2 fc0 sc0 lse8">4<span class="ff2 fs1 ls57 ws1e6 v4">mo<span class="_4 blank"> </span>dos, resp<span class="_1f blank"> </span>ectiv<span class="_39 blank"></span>amente.<span class="_f blank"> </span>F<span class="_39 blank"></span>azendo isso, con<span class="_7 blank"></span>tamos cada</span></div><div class="t m0 x0 h2 y109 ff2 fs1 fc0 sc0 ls5a ws1e7">divis\u02dc<span class="_17 blank"></span><span class="ls3 ws1e8">ao 4!<span class="ff5 ls23 wsf">.</span><span class="ls70 ws1e9">2! vezes,<span class="_d blank"> </span>p<span class="_1f blank"> </span>orque, qua<span class="_4 blank"> </span>ndo forma<span class="_4 blank"> </span>mos os mesmos<span class="_d blank"> </span>g<span class="_4 blank"> </span>rup<span class="_4 blank"> </span>os de 3</span></span></div><div class="t m0 x0 h2 y10a ff2 fs1 fc0 sc0 ls5f ws1ea">e os mesmos grup<span class="_4 blank"> </span>os 4 em outra ordem, con<span class="_2c blank"></span>tamos como se fosse outra</div><div class="t m0 x0 h2 y10b ff2 fs1 fc0 sc0 ls5a ws1e7">divis\u02dc<span class="_17 blank"></span><span class="ls26 ws1eb">ao<span class="_8 blank"> </span>em<span class="_6 blank"> </span>grup os.</span></div><div class="t m0 x0 h1f y10c ff2 fs1 fc0 sc0 ls1e ws9">Ar<span class="_9 blank"></span>e<span class="_9 blank"></span>s<span class="_9 blank"></span>p<span class="_9 blank"></span>o<span class="_9 blank"></span>s<span class="_9 blank"></span>t<span class="_9 blank"></span>a´<span class="_a blank"></span><span class="lseb">e<span class="ff5 lsec v6">C</span><span class="ff4 fs2 ls23 v7">3</span></span></div><div class="t m0 xe h18 y10d ff4 fs2 fc0 sc0 lse1 ws1ec">20 <span class="ff5 fs1 ls29 ws1ed v4">.C </span><span class="ls23 v5">3</span></div><div class="t m0 x20 h18 y10d ff4 fs2 fc0 sc0 ls21 ws1ee">17 <span class="ff5 fs1 ls29 ws1ed v4">.C </span><span class="ls23 v5">3</span></div><div class="t m0 x21 h18 y10d ff4 fs2 fc0 sc0 ls21 ws1e4">14 <span class="ff5 fs1 lsed v4">C</span><span class="ls23 v5">3</span></div><div class="t m0 x22 h18 y10d ff4 fs2 fc0 sc0 ls21 ws1e4">11 <span class="ff5 fs1 ls29 ws1ed v4">.C </span><span class="ls23 v5">4</span></div><div class="t m0 xa h18 y10d ff4 fs2 fc0 sc0 lsee">8<span class="ff5 fs1 ls29 ws1ed v4">.C </span><span class="ls23 v5">4</span></div><div class="t m0 x23 h3 y10d ff4 fs2 fc0 sc0 ls23">4</div><div class="t m0 x24 h20 y10e ff2 fs1 fc0 sc0 ls3 ws10">4!<span class="ff5 ls23 wsf">.</span><span class="ws1ef">3! <span class="lsef v6">=</span><span class="v8">20!</span></span></div><div class="t m0 x25 h21 y10e ff2 fs1 fc0 sc0 ls61 ws1f0">(3!)<span class="ff4 fs2 ls49 v9">4</span>(4!)<span class="ff4 fs2 ls49 v9">2</span><span class="ls87 ws1f1">4!2! <span class="ls23 v6">=</span></span></div><div class="t m0 x0 h2 y10f ff2 fs1 fc0 sc0 ls22 wse">=6<span class="_c blank"></span>7<span class="_c blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3 ws10">897</span>.<span class="ff2 ls3 ws10">830</span>.<span class="ff2 ls3">000.</span></span></div><div class="t m0 x0 h2 y110 ff1 fs1 fc0 sc0 ls2a ws18">Outra solu¸<span class="_17 blank"></span><span class="ls2b ws19">c\u02dc<span class="_3 blank"></span><span class="ls2c">ao:</span></span></div><div class="t m0 x0 h2 y111 ff2 fs1 fc0 sc0 ls5f ws1f2">F<span class="_b blank"></span>orme uma \ufb01la com as 20 pessoas.<span class="_35 blank"> </span>Isso automaticamen<span class="_2c blank"></span>te as divide</div><div class="t m0 x0 h2 y112 ff2 fs1 fc0 sc0 lsfd ws1f3">e<span class="_14 blank"></span>m4g<span class="_19 blank"></span>r<span class="_14 blank"></span>u<span class="_1a blank"></span>p<span class="_19 blank"></span>o<span class="_14 blank"></span>sd<span class="_14 blank"></span>e3e2g<span class="_1a blank"></span>r<span class="_1a blank"></span>u<span class="_1a blank"></span>p<span class="_19 blank"></span>od<span class="_1a blank"></span>e4<span class="_1a blank"></span>:<span class="_38 blank"> </span>a<span class="_1a blank"></span>s3p<span class="_14 blank"></span>r<span class="_1a blank"></span>i<span class="_1a blank"></span>m<span class="_1a blank"></span>e<span class="_1a blank"></span>i<span class="_1a blank"></span>r<span class="_1a blank"></span>a<span class="_1a blank"></span>s f<span class="_1a blank"></span>o<span class="_1a blank"></span>r<span class="_1a blank"></span>m<span class="_1a blank"></span>a<span class="_1a blank"></span>mu<span class="_1a blank"></span>mg<span class="_1a blank"></span>r<span class="_1a blank"></span>u<span class="_1a blank"></span>p<span class="_19 blank"></span>o<span class="_14 blank"></span>,</div><div class="t m0 x0 h2 y113 ff2 fs1 fc0 sc0 ls40 ws1f4">as 3 seguin<span class="_2c blank"></span>tes<span class="_e blank"> </span>formam<span class="_e blank"> </span>outro,<span class="_e blank"> </span>etc..<span class="_35 blank"> </span>H´<span class="_17 blank"></span><span class="ls60 ws1a4">a 20!<span class="_2d blank"> </span>mo<span class="_4 blank"> </span>dos de formar a \ufb01la.</span></div><div class="t m0 x0 h2 y114 ff2 fs1 fc0 sc0 ls41 ws1f5">En<span class="_2c blank"></span>tretanto, uma mesma divis\u02dc<span class="_3 blank"></span><span class="ls8 ws84">ao<span class="_20 blank"> </span>em<span class="_d blank"> </span>grup os<span class="_d blank"> </span>corresp onde<span class="_d blank"> </span>a<span class="_d blank"> </span>v´<span class="_17 blank"></span><span class="ls74 ws1f6">arias \ufb01las</span></span></div><div class="t m0 x0 h2 y115 ff2 fs1 fc0 sc0 ls21 ws1f7">diferen<span class="_7 blank"></span>tes, o<span class="_e blank"> </span>que<span class="_e blank"> </span>faz<span class="_e blank"> </span>com<span class="_e blank"> </span>que, n<span class="lsa7 ws1f8">o resultado<span class="_e blank"> </span>20!,<span class="_32 blank"> </span>cada divis\u02dc<span class="_17 blank"></span><span class="ls2f ws1f9">ao tenha</span></span></div><div class="t m0 x0 h2 y116 ff2 fs1 fc0 sc0 ls21 wsf6">sido contada v´<span class="_17 blank"></span>a<span class="_4 blank"> </span>rias v<span class="_7 blank"></span>ezes.<span class="_e blank"> </span>D<span class="_4 blank"> </span>ev<span class="_2c blank"></span>emo<span class="_4 blank"> </span>s co<span class="_4 blank"> </span>rrigir nossa<span class="_8 blank"> </span>contagem dividindo</div><div class="t m0 x0 h2 y117 ff2 fs1 fc0 sc0 ls2d ws199">o<span class="_d blank"> </span>resultado<span class="_20 blank"> </span>p elo<span class="_20 blank"> </span>n ´<span class="_3 blank"></span><span class="ls70 ws1fa">umero de<span class="_20 blank"> </span>vezes que cada divis\u02dc<span class="_10 blank"></span><span class="lsb9 ws16f">ao<span class="_20 blank"> </span>foi con<span class="_2c blank"></span>tada.<span class="_3d blank"> </span>T<span class="_b blank"></span>ro-</span></span></div><div class="t m0 x0 h2 y118 ff2 fs1 fc0 sc0 ls3c ws1c6">cando a ordem dos elemen<span class="_7 blank"></span>tos em<span class="_d blank"> </span>cada grup<span class="_4 blank"> </span>o, o que<span class="_d blank"> </span>p<span class="_4 blank"> </span>o<span class="_1f blank"> </span>de ser feito de</div><div class="t m0 x0 h2 y119 ff2 fs1 fc0 sc0 ls3 ws10">3!<span class="ff5 ls23 wsf">.</span>3!<span class="ff5 ls23 wsf">.</span>3!<span class="ff5 ls23 wsf">.</span>3!<span class="ff5 ls23 wsf">.</span>4!<span class="_7 blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls2d ws64">4! mo<span class="_4 blank"> </span>dos, ou a ordem dos grup<span class="_1f blank"> </span>os, o que p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>de ser<span class="_d blank"> </span>feito de</span></span></div><div class="t m0 x0 h2 y11a ff2 fs1 fc0 sc0 ls3 ws10">4!<span class="ff5 ls23 wsf">.</span><span class="ls2a ws1fb">2!<span class="_8 blank"> </span>mo dos,<span class="_20 blank"> </span>a<span class="_d blank"> </span>divis\u02dc<span class="_17 blank"></span><span class="ls8 ws84">ao<span class="_20 blank"> </span>em<span class="_d blank"> </span>grup os<span class="_8 blank"> </span>n\u02dc<span class="_10 blank"></span><span class="ls14 ws1fc">ao se altera, mas a \ufb01la<span class="_d blank"> </span>sim.<span class="_27 blank"> </span>Cada</span></span></span></div><div class="t m0 x0 h22 y11b ff2 fs1 fc0 sc0 ls5a ws1e7">divis\u02dc<span class="_17 blank"></span><span class="ls26 ws1fd">ao foi,<span class="_25 blank"> </span>assim, con<span class="_2c blank"></span>tada (6!)<span class="ff4 fs2 lsc v3">3</span><span class="ff5 ls23 wsf v0">.<span class="ff2 ls3 ws10">2!</span>.<span class="ff2 ls57 ws1fe">3!<span class="_1e blank"> </span>vezes<span class="_1e blank"> </span>e<span class="_25 blank"> </span>a<span class="_25 blank"> </span>resp osta<span class="_1e blank"> </span>´<span class="_11 blank"></span><span class="lsf0">e<span class="ls3 v6">20!</span></span></span></span></span></div><div class="t m0 x26 h23 y11c ff2 fs1 fc0 sc0 ls61 ws1f0">(3!)<span class="ff4 fs2 lsc v9">4</span>(4!)<span class="ff4 fs2 ls49 v9">2</span><span class="ls87 ws1ff">4!2! <span class="ls23 v6">.</span></span></div><div class="t m0 x1 h2 y11d ff1 fs1 fc0 sc0 ls1b ws6">9) <span class="ff2 ls5f ws4f">Os adv<span class="_2c blank"></span>ers´<span class="_17 blank"></span><span class="ls21 ws200">ario<span class="_4 blank"> </span>s em cada j<span class="_4 blank"> </span>ogo p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>dem ser esco<span class="_4 blank"> </span>lhidos,<span class="_8 blank"> </span>sucessiv<span class="_39 blank"></span>a<span class="_4 blank"> </span>men<span class="_2c blank"></span>t<span class="_4 blank"> </span>e,<span class="_8 blank"> </span>de</span></span></div><div class="t m0 x0 h24 y11e ff5 fs1 fc0 sc0 lsf1">C<span class="ff4 fs2 ls23 v3">2</span></div><div class="t m0 x27 h18 y11f ff4 fs2 fc0 sc0 lse1 ws201">12 <span class="ff2 fs1 lsf2 v4">,<span class="ff5 lsf3">C</span></span><span class="ls23 v5">2</span></div><div class="t m0 x28 h18 y11f ff4 fs2 fc0 sc0 ls21 ws1e4">10 <span class="ff2 fs1 lsf4 v4">,<span class="ff5 lsf5">C</span></span><span class="ls23 v5">2</span></div><div class="t m0 x29 h18 y11f ff4 fs2 fc0 sc0 lsf6">8<span class="ff2 fs1 lsf2 v4">,<span class="ff5 lsf3">C</span></span><span class="ls23 v5">2</span></div><div class="t m0 x9 h18 y11f ff4 fs2 fc0 sc0 lsee">6<span class="ff2 fs1 lsf2 v4">,<span class="ff5 lsf3">C</span></span><span class="ls23 v5">2</span></div><div class="t m0 x2a h18 y11f ff4 fs2 fc0 sc0 lsf7">4<span class="ff2 fs1 lsf8 v4">e<span class="ff5 lsf9">C</span></span><span class="ls23 v5">2</span></div><div class="t m0 x2b h19 y11f ff4 fs2 fc0 sc0 lsf7">2<span class="ff2 fs1 ls26 ws202 v4">mo dos.<span class="_27 blank"> </span>No<span class="_d blank"> </span>en<span class="_7 blank"></span>tan<span class="_2c blank"></span>to,<span class="_f blank"> </span>ass<span class="_7 blank"></span>im<span class="_d blank"> </span>con<span class="_2c blank"></span>tamos<span class="_20 blank"> </span>cada</span></div><div class="t m0 x0 h2 y120 ff2 fs1 fc0 sc0 ls71 ws7b">po<span class="_7 blank"></span>s<span class="_2c blank"></span>s<span class="_2 blank"></span>´<span class="_1a blank"></span><span class="ls3a ws32">\u0131v<span class="_2c blank"></span>el<span class="_d blank"> </span>ro da da<span class="_8 blank"> </span>6!<span class="_2a blank"> </span>vezes,<span class="_d blank"> </span>j´<span class="_17 blank"></span><span class="ls3b ws1f1">a que con<span class="_7 blank"></span>tamos diferen<span class="_2c blank"></span>tes<span class="_d blank"> </span>ordens dos jogos</span></span></div><div class="t m0 x0 h25 y121 ff2 fs1 fc0 sc0 lsfe ws108">como<span class="_1d blank"> </span>se<span class="_23 blank"> </span>fossem<span class="_1d blank"> </span>ro dadas<span class="_1d blank"> </span>diferen<span class="_2c blank"></span>tes.<span class="_f blank"> </span>A<span class="_1d blank"> </span>respo sta<span class="_23 blank"> </span>´<span class="_10 blank"></span><span class="lsfa">e<span class="ff5 lsfb v6">C</span><span class="ff4 fs2 ls23 v7">2</span></span></div><div class="t m0 x2c h18 y122 ff4 fs2 fc0 sc0 lse1 ws1ec">12 <span class="ff5 fs1 ls29 ws1ed v4">.C </span><span class="ls23 v5">2</span></div><div class="t m0 x2d h18 y122 ff4 fs2 fc0 sc0 ls21 ws1ee">10 <span class="ff5 fs1 ls29 ws1ed v4">.C </span><span class="ls23 v5">2</span></div><div class="t m0 x2e h18 y122 ff4 fs2 fc0 sc0 lsf6">8<span class="ff5 fs1 ls29 ws1ed v4">.C </span><span class="ls23 v5">2</span></div><div class="t m0 x2f h18 y122 ff4 fs2 fc0 sc0 lsee">6<span class="ff5 fs1 ls29 ws1ed v4">.C </span><span class="ls23 v5">2</span></div><div class="t m0 x30 h18 y122 ff4 fs2 fc0 sc0 lsf6">4<span class="ff5 fs1 ls29 ws1ed v4">.C </span><span class="ls23 v5">2</span></div><div class="t m0 x31 h3 y122 ff4 fs2 fc0 sc0 ls23">2</div><div class="t m0 x26 h23 y123 ff2 fs1 fc0 sc0 ls3 ws203">6! <span class="ls23 v6">=</span></div><div class="t m0 x14 h2 y124 ff2 fs1 fc0 sc0 ls3">12!</div><div class="t m0 x0 h21 y125 ff2 fs1 fc0 sc0 lsfc">2<span class="ff4 fs2 ls49 v9">6</span><span class="ff5 ls23 wsf">.</span><span class="ls3 ws204">6! </span><span class="lsae ws13f v6">=1<span class="_1b blank"></span>0<span class="_c blank"></span><span class="ff5 ls23 wsf">.<span class="ff2 ls3">395</span></span></span></div><div class="t m0 x0 h2 y126 ff1 fs1 fc0 sc0 ls2a ws18">Outra solu¸<span class="_17 blank"></span><span class="ls2b ws19">c\u02dc<span class="_3 blank"></span><span class="lsff ws205">ao<span class="ff2 ls23">:</span></span></span></div><div class="t m0 x0 h2 y127 ff2 fs1 fc0 sc0 ls14 ws206">Colo<span class="_4 blank"> </span>cando os 12 times em \ufb01la automaticamen<span class="_7 blank"></span>te formamos os 6<span class="_d blank"> </span>jogos</div><div class="t m0 x0 h2 y128 ff2 fs1 fc0 sc0 ls32 ws207">da ro<span class="_4 blank"> </span>dada.<span class="_34 blank"> </span>No en<span class="_7 blank"></span>tan<span class="_2c blank"></span>to,<span class="_e blank"> </span>a mesma<span class="_f blank"> </span>ro<span class="_1f blank"> </span>dada<span class="_d blank"> </span>´<span class="_10 blank"></span><span class="ls100 ws208">ec<span class="_11 blank"></span>o<span class="_14 blank"></span>n<span class="_11 blank"></span>t<span class="_11 blank"></span>a<span class="_11 blank"></span>d<span class="_11 blank"></span>av<span class="_14 blank"></span>´<span class="_12 blank"></span><span class="ls70 ws209">a<span class="_4 blank"> </span>rias v<span class="_7 blank"></span>ezes;<span class="_32 blank"> </span>os</span></span></div><div class="t m0 x5 h2 y129 ff2 fs1 fc0 sc0 ls23">9</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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