Wood County reporter. [volume] (Grand Rapids [i.e. Wisconsin Rapids], Wis.) 1857-1923, 1888-02-23
BUDGET OF PARADOXES.

CAloUos AOdOlL2 dUOuU Gllc
world in a verbal form, and occa-
sionally even appears in print, a GER
tain class of propositions or queries,
of which the object is to puzzle the
wits of the unWary listener, or to be-
guile him into giving an absurd reply.
Many of these are very old, and some
are excellent. Instances will readily
occur. Who, for example, has not,
at some period in his existence, been
asked the following question:: ''If a
goose weighs ten pounds and a half
its own weight, what is the weight of
the gooseP" And who has not been
tempted to reply on the instance, fif-
teen pounds?-the correct answer
being, of course, twenty pounds. In
deed, it is astonishing what very
simple query will catch a wise man
mapping. Even the following have
been known to succeed.
''How many days would it take to
cut up Il piece of cloth fifty yards long,
one yard being cut off every day?"
"A snail, climbing up post TWEEN
ty 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?"
Or again:
"A wise man having a window one
yard wide, and requiring more light,
enlarged his window to twice its for
mer size; yet the window was still
only one yard high and one yard
wide. How was this dOne?'
This is catch question in geometry,
as the preceding were catch questions
in arithmetic-the window being dia-
mond shaped at first, and afterwards
made square. As to the two former,
perhaps tits scarcely necessary serious
ly to point out that the answer to the
first is not fifty days, but forty-nine;
and to the second, not twenty days,
but sixteen-since the snail who gains
one foot each day for fifteen days
climbs on the sixteenth day to the top
of the pole, and there remains.
Such examples are plentiful, and
occasionally both curious and anus
ing. But the purpose of the following
paper is to illustrate class of prob
lens of rather different kind. There
are certain problems which are in no
way catch questions (any problem in
yolying a mere verbal bubble is of
course out of court by it's own innate
yileness), and which, though at first
sight extremely simple, often requires
considerable ingenuity to arrive at q
correct result. Take for example the
following:
"A man walks around a pole, on
the top of which is q monkey. As the
man moves the monkey turns around
on the top of the pole SO as still to
keep face to face with the man.
Query: When the man has got round
the pole, has he. or has he not gone
round the monkev?"
The answer which will occur 1t first
sight to most persons is that the man
has not gone round the monkey, since
he has never been behind it. The cor
rect answer, however, as decided by
Knowledge, 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 has not, so far as the
writer is aware, hitherto appeared in
print: "A train standing on an in
cline is just kept stationary by an en-
CINE which is not sufficiently power
full to draw it up the incline. a sec
ond engine of the same power as the
first, is then brought up to assist by
pushing the train from behind, and
the engines together take the train up
tue incline. Suppose the carriages to
be linked together by loose chains, so
that when the engine in front is act
ing the chains are stretched and the
buffers between the carriages are sep
arated, then, when the train is NOV
ing under action of two engines the
buffers must be either together OF
apart. Wkscb are they?
1t they were apart, the engine be-
behind the train is evidently doing no
work. If they are together, then the
engine in front is doing none. But
neither engine alone can move the
train. Why, then does the train
move?'
The following was once asked at q
university wine-party by q now we'll
known senior wrangler: Suppose
three snakes, each of which is swal-
lowing another by the tail, so that the
three form 4 circle-then as the swal-
lowing process continues, the circle
evidently grows smaller and smaller
Now, if they thus continue to swallow
each other, aChdt aCiI eventually become
of the SnGkeS?"
Of course, it is clear that either the
swallowing process must stop some
where, or that the snakes will vanish
down each others throats. At what
point then, will the swallowing cease?
If the reader finds himself ready on
the spot with a clear and precise an
swer to this question he will have
proved himself of 4 reader wit than
the guests of the aforementioned
wine-party. A little consideration,
however, will probably be sufficient
to clear the mystery. and, like the
preceding enigma of the railway, the
problem may be safely LETT to the ex-
abingdon of the ingenious.
(Which, at any given moment is
moving forward fastest, the top of q
coach-wheel or the bottom?" To this
apparently very simple question nine
persons out of ten, asked at random,
will give an incorrect reply. For at first
sight it appears evident that both the
top and the bottom of the wheel must
be moving forward ut the same rate
namely, the speed ut which the car
riage is travelling. But little thought
will show that this is far from being
the ease. A point on the bottom of
the wheel is, in fact, by direction of
its motion round the axis, moving
backward, in IN opposite direction to
that in which the carriage is progress
Ing, and is consequently III space;
while a point on top of the wheel is