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(273) 1

Part of 1990 Tournament Of Towns

Problems(1)

TOT 273 1990 Autumn O S1 pos/ integers 1-n^2 in nxn chessboard

Source:

6/8/2024
The positive integers from 11 to n2n^2 are placed arbitrarily on the squares of a chess board with dimensions n×nn\times n. Prove that there are two adjacent squares (having a common vertex or a common side) such that the difference between the numbers placed on them is not less than n+1n + 1.
(N Sedrakyan, Yerevan)
combinatorics