Problem #PRU-64652

Problems Methods Pigeonhole principle Pigeonhole principle (other) Combinatorics Dissections, partitions, covers and tilings Tilings with ordinary and domino tiles

Problem

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?