Answer to Riddle #62: Climbing Snail, 3 Steps Forward, 2 Steps Back

62. A snail is at the bottom of a 30 foot well. Every hour the snail is able to climb up 3 feet, then immediately slide back down 2 feet. How many hours does it take for the snail to get out of the well?

There's a whole raft of puzzles of this form, usually 3 steps forward, usually 2 steps back; It might be walking uphill in the snow, something like that, there's a tiny little catch, lets take a look:

snail climbing a wallBefore reading the answer can I interest you in a clue?

The plan here is that you will slightly out smart yourself and having worked out that the net speed is +1 foot per hour you will just use common sense and say 30feet at 1 foot an hour is 30 hours...

The answer is actually 28 hours. Why? The logic is true, 1 foot an hour for, let's say, 27 hours/feet, then at the end of the 28th hour the snail climbs 3 feet (making 30 feet,) and reaches the top before, this time, not sliding back.

Assumptions

The wording on these types of puzzle is always very precise. Or at least includes specific phrases like 'immediately slide back down' these are obviously physical nonsense but they do point to the answer. The the plan to my mind is to work out the obvious route up to a safe distance from the end, in this case 27 hours/feet then model the exact behaviour. ie that in the next hour it climbs 3 feet and is instantly at the top of the well. Read the wording carefully.

I'd like to build a list of examples of this specific type of puzzle, if you see one I'd appreciate an email or hit me up on twitter @nigelcoldwell.





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