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Indian RMO 2011: Question 2

Source:

December 4, 2011

Problem Statement

Let (a1,a2,a3,...,a2011)(a_1,a_2,a_3,...,a_{2011}) be a permutation of the numbers 1,2,3,...,20111,2,3,...,2011. Show that there exist two numbers j,kj,k such that 1≤j<k≤20111\leq{j}<k\leq2011 and ∣aj−j∣=∣ak−k∣|a_j-j|=|a_k-k|
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