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A permutation with distinct differences

Source: Romanian TST 5 2008, Problem 1

June 13, 2008
inductiongraph theoryalgebra proposedalgebra

Problem Statement

Let n n be a nonzero positive integer. Find n n such that there exists a permutation σ∈Sn \sigma \in S_{n} such that \left| \{ |\sigma(k) \minus{} k| \ : \ k \in \overline{1, n} \}\right | = n.
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