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A simple version of the puzzle of the climbing snail is familiar to
everybody. We were all taught it in the nursery, and it was apparently
intended to inculcate the simple moral that we should never slip if we
can help it. This is the popular story. A snail crawls up a pole 12 feet
high, ascending 3 feet every day and slipping back 2 feet every night.
How long does it take to get to the top? Of course, we are expected to
say the answer is twelve days, because the creature makes an actual
advance of 1 foot in every twenty-four hours. But the modern infant in
arms is not taken in in this way. He says, correctly enough, that at the
end of the ninth day the snail is 3 feet from the top, and therefore
reaches the summit of its ambition on the tenth day, for it would cease
to slip when it had got to the top.
Let us, however, consider the original story. Once upon a time two
philosophers were walking in their garden, when one of them espied a
highly respectable member of the Helix Aspersa family, a pioneer in
mountaineering, in the act of making the perilous ascent of a wall 20
feet high. Judging by the trail, the gentleman calculated that the snail
ascended 3 feet each day, sleeping and slipping back 2 feet every night.
"Pray tell me," said the philosopher to his friend, who was in the same
line of business, "how long will it take Sir Snail to climb to the top of
the wall and descend the other side? The top of the wall, as you know,
has a sharp edge, so that when he gets there he will instantly begin to
descend, putting precisely the same exertion into his daily climbing down
as he did in his climbing up, and sleeping and slipping at night as
before."
This is the true version of the puzzle, and my readers will perhaps be
interested in working out the exact number of days. Of course, in a
puzzle of this kind the day is always supposed to be equally divided into
twelve hours' daytime and twelve hours' night.