Climbing stairs

A staircase has 1010 steps; you climb 11 or 22 steps at a time. How many distinct ways are there to reach the top?

Show hints (2)+
  1. Condition on the size of the last step.
  2. Fibonacci recurrence Wn=Wn−1+Wn−2W_n = W_{n-1}+W_{n-2}.

Answer

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89

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