The Cambria freeman. [volume] (Ebensburg, Pa.) 1867-1938, 1891-06-19
TO CATCH THE UNWARY.
Many Old and New Paradoxes
That Are Interesting.
Tets for the Wits Of Your Tri-nds-Bright
rrobiem. That Arc PuzzIinG Yet
Easy SoIve-An Old Rule
with No Exception.

small dinner party one evening not
long ago. the subject of paradoXes was
introduced. IL was a matter of consid-
crablc comment to those present what
n large 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
unwarv 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
a 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-
doubtcdly some readers will find a num-
ber of questions which they have nevor
before heard. Nha has net NJ some
period of his existence puzzled his brain
over this query:
If Il goose weighs ten pounds and
half it, own weight. what i the weight
of the goose?
Many persons have undoubtedly been
tempted to answer fifteen pounds. when
the correct answer. of course. il twenty
pounds as they discover after giving
the problem Ettlc t,1ought. An eX-
cecdingly wise r2an has sometimes been
caught 10y a YER. simple question of
this sort. The following for example:
How many days would it take To cut
up piece of cloth -Sfty yards long, one
yard being cut off every day?
OR this:
\ snail climbing sp post twenty feet
high ascends five feet every day and
slips down four feet every night How
long will il take the snail to reach the
top of the post2
These are simple questions in
arithmetic, as4d yet, how many per-
sons would answer fifty days, instead
of forty-nine TO the first one. and
twenty instead os sixteen To the last
one. IL j. perhaps scarcely necessary
tn point out that the snail would gain
one foot day for fifteen days, and on
the sixteenth day reach the top of
the pole, and there. of course, remain.
Here il one of different sort, but
none the less puzzling:
\ man walks round a pole, ON the
top OF which il a monkey. A. the man
moves. the monkey turns round on the
top ot the pole. 50 as still TO keep face
To- face with the man. When the man
has gone round the pole. has he or has
H. not. gone round the monkey?
As either answer to this question may
be upheld with strong and logical
arguments the reader i left To decide
the question for himself.
Which, 1T any given moment. i NOV
ing forward faster. the top of coach
wheel. or the bottom?
The answer to this question seems
simple enough. but probably nine per
sons ont IF ten. asked at random. would
give the wrong reply. Ii would appear
at first ight that the top and bottom
must bc moving at the same rate; that
is, the speed of the carriage. But by n
little thought il will be discovered that
the bottom s,f the wheel il. in fact, by
the direction of its motion around its
axis moving backward, in an opposite
direction To that which the carriage is
advancing. and is consequently station
AIRY 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 IF Zeno, by which he sought
to prove that all motion is impossible
"a body" he argued, must move
either in place where il is or in a
place where il is not. Now body in
the place where IL is is stationary and
cannot be in motion, nor, obviously,
can il bc in melton in the place where
il is not. Therefore il cannot move at
all"
Bodies do move, however. and that is
a sufficient answer To- the ingenious
philosopher. Another paradox which
has been inherited from the Greeks
that of Achilles and the tOrtoise-is
familiar.
Achilles (the swift-footed) allows the
tortoise a hundred yards start and
runs ten yards while the tortoise runs
one. Now. when Achilles has run a
hundred yards the tortoise has run
ten yards, and il therefore still
that distance ahead. When Achil-
les has run these ten yards,
the tortoise has run one yard When
Achilles has run the one ward. the tor
toise has run one-tenth Of yard And
when Achilles has run the one-tenth of
n yard the tortoise has run oue-hun-
dredth. II is only necessary to con-
tinue the same process of reasoning TO
prove that Achilles can never overtake
tha tortoise
OF course, IL is q fact that Achilles does
,vertak- the tortoise, notwithstand-
ng this apparently logical reasoning To
he contrary. The conclusion Of that
paradox is somewhat different from the
following, although in some ways sim
lar to il:
a man owes four cents. HE pays two
'ents one day, one cent the next. one
lalf cent the next and 81 on. on.-half
'ech day of the debt Now. although