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Danube Mathematical Competition 2007 Problem 1

Source: a bit similar to IMO 2007 Pr. 1

December 8, 2007
algebra proposedalgebra

Problem Statement

Let n≥2 n\ge2 be a positive integer and denote by Sn S_n the set of all permutations of the set {1,2,…,n} \{1,2,\ldots,n\}. For σ∈Sn \sigma\in S_n define l(σ) l(\sigma) to be \displaystyle\min_{1\le i\le n\minus{}1}\left|\sigma(i\plus{}1)\minus{}\sigma(i)\right|. Determine max⁡σ∈Snl(σ) \displaystyle\max_{\sigma\in S_n}l(\sigma).
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