OlympiadHardCombinatorics7–9
Two opposite corner squares are cut from an 8 \times 8 chessboard. What is the largest number of 1 \times 2 dominoes that can be placed on what remains, without overlaps and without hanging over the edge?
Retiram-se dois quadrados de cantos opostos de um tabuleiro 8 \times 8. Qual é o maior número de dominós 1 \times 2 que se podem colocar no que resta, sem sobreposições e sem sair do tabuleiro?
Answer options
Solution
Step 1 of 3
- 1.Opposite corners of a chessboard share a colour, so the 62 remaining squares split into 32 of one colour and 30 of the other.