关于n×n棋盘填数问题的一个命题

A proposition on filling the numbers in the squares of the n×n chessboard

证明如果在n×n棋盘的方格中每一格分别填入数1,2,…,n2(n 2),使得任意两个相邻的方格中的两数之差都不超过n,则相邻的方格中的两数之差恰等于n的方格对至少有2(n-1)对.

In this paper, the proposition is proved that if the numbers 1, 2, …, n^2 （n≥2） are filled in every square of n×n chessboard, with difference of two numbers in any consecutive squares below n, then at least 2（n=1） pairs of consecutive squares are got, in which the difference of two numbers is just equal to n.