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IMO 1987 Problem 1

  • Day 1

Let pn(k)p_n(k) be the number of permutations of the set {1,2,3,…,n}\{1,2,3,\ldots,n\} which have exactly kk fixed points. Prove that ∑k=0nkpn(k)=n!\sum_{k=0}^nk p_n(k)=n! .

Dataset text AI-MO AoPS. Quoted with source.

Official text: IMO 1987 official English paper, page 1.

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