MathDB

On a

5 \times 5

board, pieces made up of

4

squares are placed, as seen in the figure, each covering exactly

4

squares of the board. The pieces can be rotated or turned over. They can also overlap, but they cannot protrude from the board. Suppose that each square on the board is covered by at most two pieces. Find the maximum number of squares on the board that can be covered (by one or two pieces).
https://latex.artofproblemsolving.com/c/8/f/c8fb3b700756487f866f9e74a6b5e20d7db9f8a5.png

Problem Statement