Compositions

MediumCombinatorics~4m

In how many ways can 66 be written as an ordered sum of positive integers (for example 1+51+5 differs from 5+15+1)?

Show hints (2)+
  1. Think of nn unit blocks with n−1n-1 gaps between them.
  2. Each gap independently has a divider or not ⇒ 2n−12^{n-1}.

Answer

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32

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