MathDB
Tiling game again

Source: 2023 Japan TST p2

July 21, 2023
combinatorics

Problem Statement

Consider a tile consisting of 20232023 squares arranged as shown in the figure. Place several of these tiles on a 2023×20232023\times 2023 grid such that they do not overlap. Find the maximum possible number of tiles that can be placed. Note that the tiles can be rotated but must not extend beyond the grid.