MathDB

1

Part of 2023 Japan MO Finals

Problems(1)

Overlapping game

Source: 2023 Japan MO Finals 1

2/11/2023
On 5×55\times 5 squares, we cover the area with several S-Tetrominos (=Z-Tetrominos) along the square so that in every square, there are two or fewer tiles covering that (tiles can be overlap). Find the maximum possible number of squares covered by at least one tile.
combinatorics