Belmont chronicle. [volume] (St. Clairsville, Ohio) 1855-1973, 1888-02-23
BUDGETOF PARAOOXES.

N
Propositions or Queries. OF which the Oh
icct is to puzzle tae wits of the unwary
listener. or to beguile him into giving an
absurd reply. Many Of these are very
old, and some are excellent.
Who. for example. has not. AT some
period Of his existence. been asked the
following question: If goose weighs
10 lbs. and half its own weight, what is
the weight of the g0ose:' And who has
nat been tempted to reply on the instant.
Il lbs: The correct answer being. Of
course. 20 lbs.
Indeed. it is astonishing what very
simple query will sometimes catch wise
man mapping. Even the following have
been known 10 succeed:
How MANY days would il take to cut
np a piece Of cloth - wards long. one
yard being cut off every day:
Or again:
a snail climbing up a post % feet
high. ascends ) feet every day. and slips
down feet every night How long
viii the snail take to reach the top OF
the post:'
Or again:
~ wise man having a window one
ward high. and one yard wide. and re-
curing more light. enlarged his window
to twice its former size; yet the window
was still only one yard high and one
ward wide How was this done:"
This is a catch-question in geometry,
as the preceding were catch questions in
arithmetic-th window being diamond
shaped at first, and afterwards made
square.
As to the two former. perhaps ii is
scarcely necessary seriously to point out
that the answer to the first is not 80
days. but 10: and to the second. not 20
DAYS. but 16-since the snail, who gains
one foot each day for - days. climbs on
the 10Th day to the top of the pole, and
there remains.
Such examples are plentiful, and oc-
casionally both curious and amusing.
But there are certain problems which
are in no way catch questions. and which
though at first sight extremely simple,
often require considerable ingenuity 70
arrive at correct result. Take FOR eX-
ample the following:
~ nan walks round 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 monkey
The answer which will occur at first
sirlt to most persons is that the man
has not gone around the monkey. since
he has never been behind ii. The cor
rect answer, however. as decided by a
leading science publication. in the pages
Of which this momentous question has
been argued. is that the man has gone
round the monkey in going round the
pole.
The following was once asked at a
university wine-party:
"Suppose three snakes, each Of which
is swallowing another by the tail, 50 that
the three form a circle-then. rs the
swallowing process continues the circle
evidently grows smallerand smaller Now
if they thus continue to swallow each
other, what VIII eventually become Of
the snakGs!'
Of course it is clear that either the
swallowing process must stop some
where. or that the snakes will vanish
down each others throats. vt what
point. then, will the swallowing cease:
If the reader finds himself ready or
the s,at-u-ith clear and precise answer
to this question he will have proved hing
self of a reader wit than the guests Of
the above mentioned wineparty. i lit
tie consideration, however, will proba
ably be sufficient to clear up the mystery,
and the problem may safely be left to
the examination of the ingenious.
4 paradox familiar to the Greeks
that of Achilles and the tortOise-is well
known. Achilles the swift-footed) al
lows the tortoise d hundred yards start,
and runs ten yards while the tortoise
runs one Now, when Achilles has run
a hundred yards the tortoise has run one
ward. and is, therefore, still that distance
ahead. When Achilles has run these
ten Yards. the tortoise has run one yard.
When Achilles has run the one yard, The
the tortoise has run one-tenth OF a yard.
And when Achilles has run the one
tenth OF yard, the tortoise mas run one
hundredth. 1t is only necessary to con
tinue the same process of reasoning 70
prove that Achilles can never overtake
the tortoise.
\ much better paradox. though some
what of the same kind. runs as follows:
~ man. who owes Il shilling, proceeds
to pay it at the rate of siXpence the first
day. threepence the next day, three
farthingS the next, and SO On-paying
each day half the sum he paid the day
before Supposing him to be furnished
with counters of small value, SO rs to be
able readily to pay fractions OF penny,
how long would it take him to pay the
shillins!" The answer is that he would
never pay it, It is true that he viii pay
elevanpence-f -farthing in four days. But
the remaining three farthings he can
never pay.
This paradox differs from the preced-
ing in one important particular, and de
serves to be called a better paradox for
this reason. that we know that Achilles.
in spite of ali reasoning, viii certainly
oyerfake the tortoise. But il is mathe
maticaliy demonStrable that the debtor, |
under such circumstances, can never pay |
his shilling, even though he should be
endued with the gift of immortality.
IF Dicks father is Toms son what
relation is Dick to Tom!'
This familiar query is too obvious OF
solution to deserve more than passing /
mention. The following, however, Of
the same class. will be found very much
more fatal. \ man standing before a
portrait says Of it:
''sisters and brothers have none
Yet that mans father Is by fathers son
What relation is the speaker to the
person depicted in the portraitt II is
quite remarkable how often the answer
is given, that the portrait represents the
speaker himself. As a matter Of fact it
raprpsaDfS tbh sneakers Sen.