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Labelling triangles of an (n+1)-gon

Source: Kürschák 1985, problem 1

July 27, 2014
combinatorics unsolvedcombinatorics

Problem Statement

We have triangulated a convex (n+1)(n+1)-gon P0P1…PnP_0P_1\dots P_n (i.e., divided it into n−1n-1 triangles with n−2n-2 non-intersecting diagonals). Prove that the resulting triangles can be labelled with the numbers 1,2,…,n−11,2,\dots,n-1 such that for any i∈{1,2,…,n−1}i\in\{1,2,\dots,n-1\}, PiP_i is a vertex of the triangle with label ii.
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