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第42届普特南数学竞赛题中有这样一道试题:一个8×8的格子棋盘C中,若两个方格有公共顶点或公共边,则称它们是相连的,将数1,2,……,64分别填入每个格子,便得到C的一种标号,若对C的每一种标号,两个相连方格标号数的差至多为g,则称g为一个C-间隙,试定出最小的C-间隙C_g。此题可给出几种不同的解法,但有的方法很繁,本文把该题推广到一般情形n×n的格子棋盘中加以证明,其目的是用图标号的思想给出这类问题一种简捷、有效的一般思
In the 42nd putnam math contest title, there is a question like this: In an 8 × 8 grid checkerboard C, if two squares have common vertices or common edges, they are said to be connected, and the numbers 1,2, ......, 64 fill in each grid, respectively, to get a label of C, if for each type of C, the difference between the number of two connected squares is at most g, then g is a C-gap, Test the minimum C-gap C_g. This question can give several different solutions, but some methods are very complicated. This article generalizes this problem to a general case n×n grid checkerboard. The purpose is to give this kind of problem with the icon number idea. Simple, effective general thinking