This is a variation of a famous problem that first appeared in an arithmetic textbook published in Nuremburg in 1561. A snail has fallen into a dry well twenty-one meters deep. It starts to climb the wall to escape. Each day it climbs seven meters, but, at night, while it sleeps, it slides back two meters. On what day will the snail finally escape the well?
Solution
The snail’s net gain each day is five meters. With this in mind, the quick way to solve this problem would seem be simply to say that it therefore takes four days to rise twenty meters, so it will get out on the fifth day.
A problem this well known, however, can not be so simple. The snail’s net gain is indeed five meters each day, so it will be at five meters at the end of the first day, ten at the end of the second, and fifteen at the end of the third. It then begins the fourth day by climbing seven more meters. This puts the snail at twenty-two meters, so it is out of the well on the fourth day and does not have to worry about sliding back down two meters that night.