MathDB

4

Part of 1991 ITAMO

Problems(1)

4 black squares in every row and column of a 8x8 board (bw)

Source: 1991 ITAMO p4

1/31/2020
The squares of an 8×88 \times 8 board are colored black and white in such a way that every row and every column contains exactly four black squares. Prove that the number of pairs of neighboring white squares is the same as the number of pairs of neighboring black squares. (Two squares are neighboring if they have a side in common.)
combinatoricsColoring