MathDB

4

Part of 1988 IMO Shortlist

Problems(1)

n x n numbered chessboard

Source: IMO ShortList 1988, Problem 4, Czech Republic 1, Problem 6 of ILL

10/22/2005
An n×n,n≥2 n \times n, n \geq 2 chessboard is numbered by the numbers 1,2,…,n2 1, 2, \ldots, n^2 (and every number occurs). Prove that there exist two neighbouring (with common edge) squares such that their numbers differ by at least n. n.
combinatoricsIMO ShortlistExtremal Graph Theorygraph theorypermutation