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(308) 5

Part of 1991 Tournament Of Towns

Problems(1)

TOT 308 1991 Autumn A J5 coloured cells in 9x9 square

Source:

6/9/2024
A 9×99 \times 9 square is divided into 8181 unit cells. Some of the cells are coloured. The distance between the centres of any two coloured cells is more than 22. (a) Give an example of colouring with 1717 coloured cells. (b) Prove that the numbers of coloured cells cannot exceed 1717.
(S. Fomin, Leningrad)
combinatoricsColoring