MathDB

Each cell of a

10 \times 10

board is painted red, blue or white, with exactly twenty of them red. No two adjacent cells are painted in the same colour. A domino consists of two adjacent cells, and it is said to be good if one cell is blue and the other is white. (a) Prove that it is always possible to cut out

30

good dominoes from such a board. (b) Give an example of such a board from which it is possible to cut out

40

good dominoes. (c) Give an example of such a board from which it is not possible to cut out more than

30

good dominoes.

Problem Statement