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Number of Permutations

Source: Turkey TST 2014 Day 1 Problem 1

March 12, 2014
inductionanalytic geometrygraphing linesslopecombinatorics proposedcombinatorics

Problem Statement

Find the number of (a1,a2,...,a2014)(a_1,a_2, ... ,a_{2014}) permutations of the (1,2,...,2014)(1,2, . . . ,2014) such that, for all 1≤i<j≤20141\leq i<j\leq2014, i+ai≤j+aji+a_i \leq j+a_j.
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