2005 Alabama ARML TST Problems/Problem 10
Problem
When Jon Stewart walks up stairs he takes one or two steps at a time. His stepping sequence is not necessarily regular. He might step up one step, then two, then two again, then one, then one, and then two in order to climb up a total of 9 steps. In how many ways can Jon walk up a 14 step stairwell?
Solution
He can either take 14 one-steps, or 12 one-steps and 1 two-step, etc., so we have
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