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A Child and a Staircase
Posted 21 June 2012 - 05:21 PM
Posted 22 June 2012 - 01:38 AM
Since we can solve this with either Fibonacii numbers or combinations, we can conclude that
F10 = C(10,0) + C(9.1)+ ...+c(5.5).
More generally Fn = C(n,0) + C(n-1.1) + C(n-2,2) + ... as long as the first number is no les than the second.
NOTE If you interpet the question to mean 10 steps plus the upper landing the answer would be F11, a point one poster raised. In addition if we distinquish between first strride right foot and first stride left we would double our answer.
Posted 22 June 2012 - 04:56 AM
- Bertrand Russell
Posted 22 June 2012 - 05:36 AM
Posted 06 January 2013 - 05:27 PM
I think 89 is correct. Here's a simple C# implementation that you can test out if you want to use LinqPad:
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