MathDB
Total number of placements

Source:

August 29, 2010
linear algebramatrixcombinatorics proposedcombinatorics

Problem Statement

The integers 1,2,⋯ ,n21, 2, \cdots, n^2 are placed on the fields of an n×nn \times n chessboard (n>2)(n > 2) in such a way that any two fields that have a common edge or a vertex are assigned numbers differing by at most n+1n + 1. What is the total number of such placements?
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