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at least four 2x2 squares have sum greater than 100 , in a 8x8 board

Source: 1977 Swedish Mathematical Competition p5

March 26, 2021
combinatoricssquare table

Problem Statement

The numbers 1,2,3,...,641, 2, 3, ... , 64 are written in the cells of an 8×88 \times 8 board (in some order, one per cell). Show that at least four 2×22 \times 2 squares have sum greater than 100100.
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