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## Homework Statement

Prove that the number of permutations p on the set {1,2,3,...,n} with the property that |p(k)-k| [tex]\leq[/tex] 1, for all 1[tex]\leq[/tex]k[tex]\leq[/tex]n, is the fibonacci number f[tex]_{n}[/tex]

## The Attempt at a Solution

I guess I don't understand what it's asking. I thought I knew what a permutation was... but now I'm really confused. Can someone please restate this problem in a way that maybe I could understand? Thanks a lot!