# 2020-03 Graceful permutations

A permutation $$\pi : [n]\rightarrow [n]$$ is graceful if $$|\pi(i+1) – \pi(i)| \neq |\pi(j+1)-\pi(j)|$$ for all $$i\neq j \in [n-1]$$. For a graceful permutation $$\pi :[2k+1] \rightarrow [2k+1]$$ with $$\pi(\{2,4,\dots,2k\}) = [k]$$, prove that $$\pi(1)+ \pi(2k+1) = 3k+2$$.

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