St. Johnsbury Caledonian. [volume] (St. Johnsbury, Vt.) 1867-1919, 1888-04-05
PROBLEMS AND PARADoxEs.

1t is astonishing what very simpl
query will sometime catch wise mar
mapping, even the following have beer
| known to succeed:
How many days would it take to Gu
up piece of cloth 80 yards long, on,
yard being cut off every day 2"
! Or again:
"a snail climbing up a post 90 fee
| high, ascends five feet every day, an(
slips down four feet every night. How
| long will the snail take to reach the tor
of the post ~
Or again:
GA wise man having a window one
yard high and one yard wide and re.
quiring more light, enlarged his win
dow to twice it's former size yet the
window was still only one yard higl
and one yard WIDE"
Suppose three snakes each of which
is swallowing another by the tall, SO
that the three form a circle-then as
the swallowing process continues, the
circle evidently grows smaller and
smaller. Now, if they thus continue to
swallow each other, what will eventu-
ally become of the snakes 2"
OF different sort are the following
ga man walks around pole, on the
top of which is monkey. AS the man
moves the monkey turns round on the
top of the pole so as to still keep face
to face with the man. Query When
the man has gone round the pole, has
he, or has he not, gone round the mon
key 2"
ga train starts daily from San Fran
cisco to New York, and one daily from
New York to San Francisco, the jour
ney lasting seven days. How many
trains will traveller meet in journey
ing from San Francisco to New York;"
GA man who owes Il shilling, proceeds
to pay it at the rate of sixpence the
first day, threePence the next day,
three halfpence the next, and so on
paying each day half the amount he
paid the day before. How long would
it take him to pay the shilling ?"
AS to the catch questions above, it is
scarcely necessary to point out that
the answer to the first is not 80 days,
but 40 and to the second, not 20 days
but I6-since the snail who gains one
foot each day for Is days, climbs on
the 10th to the top of the pole, and
there remains.
In the third problem the window is
at first diamond shape, and then is
made square. The correct answer to
the fifth is that the man has gone round
the monkey in going round the pole.
In answering the train question nine
people out of ten overlook the fact that
every day during the journey a fresh
train is starting from the other end,
while there are seven on the way west
to begin with. AS to the debt, of
course, the man can never fully pay it.,
by the very terms of the problem, half
of the last previous payment still re-
naming unpaid to all eternity.
In Zeno's famous paradox he proved
that all motion is impossible, thus: ga
body must move either in the place
where it is, or in the place where it is
not. Now, a body in the place where
it is, is stationary, and cannot be in
motion; nor, obviously, can it be in
motion where it is not. Therefore, it
cannot move at ALL" 1t was of this
paradox it was said, sOIritur an1bulandO
cit is solved by walking"
The following proposition is curl
GUS one: eff there are more people in
the world than any one person has
hairs upon his head, then there must
exist at least two persons who possess
identically the same number of hairs,
to hair"
If the reader fails to perceive the
necessity of this conclusion let him first
consider, as simpler case, instead of
the hairs on mans head, the number
of teeth in his jaw. Let him suppose
"a persons to be assembled then the
full number of teeth in mans jaw be-
ing 81, it can be seen that-even if one
has has no teeth at all-there must be
at least two persons present possessed
of the same number of teeth. The ap-
plication of this example to the propo-
sitiOn in question is evident.