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A1

Part of 1954 Putnam

Problems(1)

Putnam 1954 A1

Source: Putnam 1954

7/17/2022
Let nn be an odd integer greater than 1.1. Let AA be an n×nn\times n symmetric matrix such that each row and column consists of some permutation of the integers 1,2,…,n.1,2, \ldots, n. Show that each of the integers 1,2,…,n1,2, \ldots, n must appear in the main diagonal of AA.
Putnamlinear algebramatrixpermutation