5

Part of 1977 Swedish Mathematical Competition

Problems(1)

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

Source: 1977 Swedish Mathematical Competition p5

1, 2, 3, ... , 64

are written in the cells of an

8 \times 8

board (in some order, one per cell). Show that at least four

2 \times 2

squares have sum greater than

100

combinatoricssquare table