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MathNet 2015-part-01 — 191 problems (EN–VI) Question 172

Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)

Question 172

An $8 \times 8$ board is given.

a) What is the minimum number of squares we must mark on this board so that each of its $3 \times 3$ sub-boards has at least one marked square?

b) What is the minimum number of squares we must mark on this board so that each of its $3 \times 3$ sub-boards has at least three marked squares?