We posed two puzzles for the price of one on Friday. The first can be found elsewhere on the internet, and requires a little thought; the second is an extension of the first, and is much trickier.
There is a wall nine metres high, and at the bottom of it there is a snail. The snail climbs for twelve hours, but is then tired and rests for twelve hours, before resuming its climb. In each twelve-hour climb it ascends three metres, and in each twelve-hour rest it slips back two metres. So every day it climbs three metres and slips back two.
How many days does it take for the snail to reach the top of the wall?
It’s easy to fall into the trap of taking the two metres down from the three metres up, and arriving at the conclusion that it is one metre up each day. Well it is for the first six days, and then the snail climbs three metres in the next twelve hours, reaching the top in six and a half days.
So now we can move on to the related (and harder) puzzle.
In this puzzle the same snail, having reached the top of the wall, wants to return to the bottom. How many days does it take to get back to the bottom?
Here the trap is to add the three metres the snail crawls in twelve hours to the two metres it slips in the next twelve hours, and thinking the snail descends at five metres in each day. However, this fails to account for the slippage the snail encounters while crawling.
During the climb the snail overcomes two metres of slippage while climbing a nett three metres. That is, it climbs at a rate of five metres in twelve hours.
Going down it benefits from the slippage and achieves a nett seven metres in the first twelve hours. And then slips the remaining two metres while resting, making one day in total.