# The Snail and the Wall Quiz Puzzle

Two puzzles for the price of one this week. 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?

Once you have thought about that 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?

Be warned – this is a much subtler problem.

## 1 comment

• Rich Twose

Ok then:

To climb the wall, 7.5 days

To climb down the wall, 1 day

When climbing, the snail moves up 3m, then back 2, resulting in a 1m gain each day. At the start of day 2, it begins at 1m up; day 3 it begins at 2m up and so on. This means that on day 7, it starts at 6m, and the 3m it manages to climb in the first 12 hours is enough to get it to the top and stop the timer.

When climbing the wall, the 2m per 12 hours backwards slide is always happening, even when awake. If the snail climbs up 3m in 12 hours, it actually means it climbed the equivalent of 5m, but lost 2m due to slippage whilst climbing. This means that when climbing down, it gets 5m (natural speed) + 2m (slippage) in the first 12 hours, then another 2m during the second 12 hours whilst asleep. This gives you the 9m total. The bonus here is that the snail gets to finish it’s journey whilst asleep, and wakes up just as it gets to ground level ;)