64652 – We Solve Problems

#### Pigeonhole principle (other) , Tilings with ordinary and domino tiles

Peter marks several cells on a $5 \times 5$ board. His friend, Richard, will win if he can cover all of these cells with non-overlapping corners of three squares, that do not overlap with the border of the square $($you can only place the corners on the squares$)$. What is the smallest number of cells that Peter should mark so that Richard cannot win?

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