Amusements-in-Mathematics-92

Prévia do material em texto

"The	 illustration	 is	a	 fancy	sketch	of	my	correspondent,	 'Simple	Simon,'	 in	 the
act	 of	 trying	 to	 solve	 the	 following	 innocent	 little	 arithmetical	 puzzle.	A	 race
between	a	man	and	a	woman	that	I	happened	to	witness	one	All	Fools'	Day	has
fixed	itself	indelibly	on	my	memory.	It	happened	at	a	country-house,	where	the
gardener	and	the	cook	decided	to	run	a	race	to	a	point	100	feet	straight	away	and
return.	I	found	that	the	gardener	ran	3	feet	at	every	bound	and	the	cook	only	2
feet,	but	then	she	made	three	bounds	to	his	two.	Now,	what	was	the	result	of	the
race?"
A	fortnight	after	publication	I	added	the	following	note:	"It	has	been	suggested
that	perhaps	there	is	a	catch	in	the	'return,'	but	there	is	not.	The	race	is	to	a	point
100	 feet	 away	 and	 home	 again—that	 is,	 a	 distance	 of	 200	 feet.	 One
correspondent	asks	whether	they	take	exactly	the	same	time	in	turning,	to	which
I	reply	that	they	do.	Another	seems	to	suspect	that	it	is	really	a	conundrum,	and
that	the	answer	is	that	 'the	result	of	the	race	was	a	(matrimonial)	tie.'	But	I	had
no	such	intention.	The	puzzle	is	an	arithmetical	one,	as	it	purports	to	be."
429.—PLACING	HALFPENNIES.
Here	is	an	interesting	little	puzzle	suggested	to	me	by	Mr.	W.	T.	Whyte.	Mark	off
on	a	sheet	of	paper	a	rectangular	space	5	inches	by	3	inches,	and	then	find	the
greatest	number	of	halfpennies	that	can	be	placed	within	the	enclosure	under	the
following	conditions.	A	halfpenny	is	exactly	an	inch	in	diameter.	Place	your	first
halfpenny	where	you	like,	then	place	your	second	coin	at	exactly	the	distance	of
an	inch	from	the	first,	the	third	an	inch	distance	from	the	second,	and	so	on.	No
halfpenny	may	 touch	another	halfpenny	or	cross	 the	boundary.	Our	 illustration
will	make	the	matter	perfectly	clear.	No.	2	coin	is	an	inch	from	No.	1;	No.	3	an
inch	from	No.	2;	No.	4	an	inch	from	No.	3;	but	after	No.	10	is	placed	we	can	go
no	further	in	this	attempt.	Yet	several	more	halfpennies	might	have	been	got	in.
How	many	can	the	reader	place?
430.—FIND	THE	MAN'S	WIFE.
One	 summer	 day	 in	 1903	 I	 was	 loitering	 on	 the	 Brighton	 front,	 watching	 the
people	strolling	about	on	the	beach,	when	the	friend	who	was	with	me	suddenly
drew	my	attention	to	an	individual	who	was	standing	alone,	and	said,	"Can	you
point	out	that	man's	wife?	They	are	stopping	at	the	same	hotel	as	I	am,	and	the
lady	is	one	of	those	in	view."	After	a	few	minutes'	observation,	I	was	successful
in	indicating	the	lady	correctly.	My	friend	was	curious	to	know	by	what	method
of	reasoning	I	had	arrived	at	the	result.	This	was	my	answer:—
"We	may	at	once	exclude	that	Sister	of	Mercy	and	the	girl	in	the	short	frock;	also
the	woman	selling	oranges.	It	cannot	be	the	lady	in	widows'	weeds.	It	is	not	the
lady	in	the	bath	chair,	because	she	is	not	staying	at	your	hotel,	for	I	happened	to
see	her	come	out	of	a	private	house	this	morning	assisted	by	her	maid.	The	two
ladies	in	red	breakfasted	at	my	hotel	this	morning,	and	as	they	were	not	wearing
outdoor	 dress	 I	 conclude	 they	 are	 staying	 there.	 It	 therefore	 rests	 between	 the
lady	in	blue	and	the	one	with	the	green	parasol.	But	the	left	hand	that	holds	the
parasol	 is,	 you	 see,	 ungloved	 and	 bears	 no	 wedding-ring.	 Consequently	 I	 am
driven	to	the	conclusion	that	the	lady	in	blue	is	the	man's	wife—and	you	say	this
is	correct."
Now,	as	my	friend	was	an	artist,	and	as	I	 thought	an	amusing	puzzle	might	be
devised	 on	 the	 lines	 of	 his	 question,	 I	 asked	 him	 to	 make	 me	 a	 drawing
according	to	some	directions	that	I	gave	him,	and	I	have	pleasure	in	presenting
his	production	to	my	readers.	It	will	be	seen	that	the	picture	shows	six	men	and
six	ladies:	Nos.	1,	3,	5,	7,	9,	and	11	are	ladies,	and	Nos.	2,	4,	6,	8,	10,	and	12	are
men.	These	twelve	individuals	represent	six	married	couples,	all	strangers	to	one
another,	who,	 in	walking	aimlessly	about,	have	got	mixed	up.	But	we	are	only
concerned	with	the	man	that	is	wearing	a	straw	hat—Number	10.	The	puzzle	is
to	 find	 this	 man's	 wife.	 Examine	 the	 six	 ladies	 carefully,	 and	 see	 if	 you	 can
determine	which	one	of	them	it	is.
I	 showed	 the	 picture	 at	 the	 time	 to	 a	 few	 friends,	 and	 they	 expressed	 very
different	opinions	on	the	matter.	One	said,	"I	don't	believe	he	would	marry	a	girl
like	Number	7."	Another	said,	"I	am	sure	a	nice	girl	 like	Number	3	would	not
marry	such	a	fellow!"	Another	said,	"It	must	be	Number	1,	because	she	has	got
as	far	away	as	possible	from	the	brute!"	It	was	suggested,	again,	that	it	must	be
Number	11,	because	"he	seems	to	be	looking	towards	her;"	but	a	cynic	retorted,
"For	that	very	reason,	if	he	is	really	looking	at	her,	I	should	say	that	she	is	not	his
wife!"
I	 now	 leave	 the	question	 in	 the	hands	of	my	 readers.	Which	 is	 really	Number
10's	wife?
The	 illustration	 is	 of	 necessity	 considerably	 reduced	 from	 the	 large	 scale	 on
which	it	originally	appeared	in	The	Weekly	Dispatch	(24th	May	1903),	but	it	 is
hoped	 that	 the	 details	 will	 be	 sufficiently	 clear	 to	 allow	 the	 reader	 to	 derive
entertainment	 from	 its	 examination.	 In	 any	 case	 the	 solution	given	will	 enable
him	to	follow	the	points	with	interest.