A cat accidentally falls down a hole with sloping but rough sides. It can climb out of the hole of height h metres, but for every m metres it jumps, it falls back n metres where m is always bigger than n. It can only do one jump attempt per day and it is assumed that there is a small water source available to sustain it along the way.:) That said, how many days does it require to escape the hole?
NB: the cat must be clear of the hole or above it to escape so reaching exactly level with the hole opening it will still fall back down n metres.
HINT: once the cat is clear of the hole with its last jump it will not fall back into the hole.
EX: >> h = 20; m = 5; n = 3;
>> catdays(20,5,3)
ans = 9
My cat gets out 1 day earlier on cases 3 and 4, by a claw. He reaches 25 on day 20.
I stand by my test case answers for 3 and 4 as the cat must be clear or above the hole to escape.
Hi RIchard, sorry if my conditions are a bit restrictive and you are quite clever to have realised it could be a day earlier for those test cases. Perhaps my problem is unnecessarily restrictive so if others feel the same I will revise it. :)
There are also the feelings of the cat to consider--whether it is fair to force him to spend an extra day undergoing an experiment of questionable benefit to science (and no obvious benefit to cats).
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