THE GARDENER AND THE COOK.
(
Unclassified Problems.)
A correspondent, signing himself "Simple Simon," suggested that I should
give a special catch puzzle in the issue of _The Weekly Dispatch_ for
All Fools' Day, 1900. So I gave the following, and it caused
considerable amusement; for out of a very large body of competitors,
many quite expert, not a single person solved it, though it ran for
nearly a month.
"The illustration is a fancy sketch of my correspondent, 'Simple Simon,'
in the act of trying to solve the following innocent little arithmetical
puzzle. A race between a man and a woman that I happened to witness one
All Fools' Day has fixed itself indelibly on my memory. It happened at a
country-house, where the gardener and the cook decided to run a race to
a point 100 feet straight away and return. I found that the gardener ran
3 feet at every bound and the cook only 2 feet, but then she made three
bounds to his two. Now, what was the result of the race?"
A fortnight after publication I added the following note: "It has been
suggested that perhaps there is a catch in the 'return,' but there is
not. The race is to a point 100 feet away and home again--that is, a
distance of 200 feet. One correspondent asks whether they take exactly
the same time in turning, to which I reply that they do. Another seems
to suspect that it is really a conundrum, and that the answer is that
'the result of the race was a (matrimonial) tie.' But I had no such
intention. The puzzle is an arithmetical one, as it purports to be."
Answer:
Nobody succeeded in solving the puzzle, so I had to let the cat out of
the bag--an operation that was dimly foreshadowed by the puss in the
original illustration. But I first reminded the reader that this puzzle
appeared on April 1, a day on which none of us ever resents being made
an "April Fool;" though, as I practically "gave the thing away" by
specially drawing attention to the fact that it was All Fools' Day, it
was quite remarkable that my correspondents, without a single exception,
fell into the trap.
One large body of correspondents held that what the cook loses in stride
is exactly made up in greater speed; consequently both advance at the
same rate, and the result must be a tie. But another considerable
section saw that, though this might be so in a race 200 ft. straight
away, it could not really be, because they each go a stated distance at
"every bound," and as 100 is not an exact multiple of 3, the gardener at
his thirty-fourth bound will go 2 ft. beyond the mark. The gardener
will, therefore, run to a point 102 ft. straight away and return (204
ft. in all), and so lose by 4 ft. This point certainly comes into the
puzzle. But the most important fact of all is this, that it so happens
that the gardener was a pupil from the Horticultural College for Lady
Gardeners at, if I remember aright, Swanley; while the cook was a very
accomplished French chef of the hemale persuasion! Therefore "she (the
gardener) made three bounds to his (the cook's) two." It will now be
found that while the gardener is running her 204 ft. in 68 bounds of 3
ft., the somewhat infirm old cook can only make 45+1/3 of his 2 ft.
bounds, which equals 90 ft. 8 in. The result is that the lady gardener
wins the race by 109 ft. 4 in. at a moment when the cook is in the air,
one-third through his 46th bound.
The moral of this puzzle is twofold: (1) Never take things for granted
in attempting to solve puzzles; (2) always remember All Fools' Day when
it comes round. I was not writing of _any_ gardener and cook, but of a
_particular_ couple, in "a race that I witnessed." The statement of the
eye-witness must therefore be accepted: as the reader was not there, he
cannot contradict it. Of course the information supplied was
insufficient, but the correct reply was: "Assuming the gardener to be
the 'he,' the cook wins by 4 ft.; but if the gardener is the 'she,' then
the gardener wins by 109 ft. 4 in." This would have won the prize.
Curiously enough, one solitary competitor got on to the right track, but
failed to follow it up. He said: "Is this a regular April 1 catch,
meaning that they only ran 6 ft. each, and consequently the race was
unfinished? If not, I think the following must be the solution,
supposing the gardener to be the 'he' and the cook the 'she.'" Though
his solution was wrong even in the case he supposed, yet he was the only
person who suspected the question of sex.
