Abilene weekly reflector. [volume] (Abilene, Kan.) 1888-1935, 1891-06-04
TO CATCH THE UNWARY.
Many Old and New Paradoxes
That Are Interesting.
Tests for the Wits of Your Friends-BrIght
Problems That Are Puzzling Yet
Easy to SOIvc-An Old Rule
with No Exception.

After the cigars had been lighted at
small dinner party one evening not
long ago, the subject of paradoxes was
introduced. 1t was matter of consid-
erablc comment to those present what,
a largo number of propositions, or
queries, there are floating about the
world in one form or another, which
are intended to puzzle the wits of the
unwary. Some of them are extremely
ancient, having been handed down
from the works of the Greek philosoph-
ers, and some are of recent origin. All
of them form excellent mental exercise,
as they sharpen the wits, besides being
recreation to the mind. No claim to
originality is made to the examples
given here, most of which were brought
out at the dinner mentioned, but un-
doubtedly some readers will find num-
Der of questions which they have never
before heard Who has not at some
period of his existence puzzled his brain
over this query:
If goose weighs ten pounds and
half its own weight, what Is the weight
of the goose?
Many persons have undoubtedly been
tempted to answer fifteen pounds, when
the correct answer, of course, is twenty
pounds, as they discover after giving
the problem a little thought. An ex-
ceedingly wise man has sometimes been
caught by very simple question Of
this sort. The following for example:
How many days would 1t take to cut
up piece of cloth fifty yards long, one
yard being cut off every day?
Or this:
A snail climbing up post twenty feet
high ascends five feet every day and
slips down four feet every night How
long will it take the snail to reach the
top of the post?
These are simple questions in
arithmetic, and yet, how many per-
sons would answer fifty days, instead
of forty-nine to the first one, and
twenty instead of sixteen to the last
one. 1t is perhaps scarcely necessary
to point out that the snail would gain
one foot day for fifteen days, and on
the pole, and there, of course, remain.
Here is one of a different sort, but
none the less puzzling:
A man walks round a pole, on the
top of which is a monkey. AS the man
moves, the monkey turns round on the
top of the pole, SO as still to keep face
to face with the man. When the man
has gone round the pole, has he or has
he not, gone round the monkey?
AS either answer to this question may
be upheld with strong and logical
the question for himself
Which, at any given moment, is NOV
ing forward faster, the top of a coach
wheel, or the bottom?
The answer to this question seems
simple enough, but probably nine per-
sons out of ten, asked at random, would
give the wrong reply. 1t would appear
at first sight that the top and bottom
must be moving at the same rate; that |
is, the speed of the carriage. But by a
little thought it will be discovered that |
the bottom of the wheel is, in fact, by
the direction of its motion around its |
axis, moving backward, in an opposite |
direction to that which the carriage Is /
adva ncing, and is consequently station
ary in space, while the point on top /
of the wheel is moving forward with
the doubled velocity of its own motion
around the axis and the speed at which
the carriage moves
Many persons will recall the famous
paradox of Zeno, by which he sought
to prove that all motion is impossible.
"a body" he argued, must move
either in place where it Is or in
place where it is not Now, body in
the place where It is is stationary and
cannot be in motion, nor, obviously,
IAN it be in motion in the place where
t is not. Therefore it cannot move at
all"
Bodies do move, however, and that Is
/ sufficient answer to the ingenious
Another paradox which
las been inherited from the Greeks
hat of Achilles and the tortoise-is
familiar.
Achilles (the swift-footed) allows the
ortoise a hundred yards start, and |
uns ten yards while the tortoise runs
ne. Now, when Achilles has run 4
Imdred yards the tortoise has run
en- yards, and Is therefore still
hat distance ahead. When Achil- |
IS has run these ten yards,
he tortoise has run one yard. When
Ichilles has run the one yard, the tor
oise has run one-tenth Of a yard And
vhen Achilles has run the one-tenth of
yard the tortoise has run One-hun-
redth. Il Is only necessary to con-
nue. tho same process of reasoning to
rove that Achilles can never oVertaks {
le tortoise.
OF course, it is fact that Achilles does
vertake the tortoise, nOtwithstand- ;
ng this apparently logical reasoning to {
he contrary The conclusion of that
,aradox is somewhat different from the {
ollowing, although in some ways sim
lar to it:
A man owes four cents. He pays two
ents one day, one cent the next, one.
lalf cent the next, and so on, one-half
ach day of the debt Now, although
n the fourth day he only owes one c
Iuarter of a cent, If he should be
ndued with the gift of immortality,