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Found problems: 2

2021 Indonesia MO, 8
On a $100 \times 100$ chessboard, the plan is to place several $1 \times 3$ boards and $3 \times 1$ board, so that [list] [*] Each tile of the initial chessboard is covered by at most one small board. [*] The boards cover the entire chessboard tile, except for one tile. [*] The sides of the board are placed parallel to the chessboard. [/list] Suppose that to carry out the instructions above, it takes $H$ number of $1 \times 3$ boards and $V$ number of $3 \times 1$ boards. Determine all possible pairs of $(H,V)$. [i]Proposed by Muhammad Afifurrahman, Indonesia[/i]
board combinatorics trimino grid geometry modular arithmetic

1981 Bundeswettbewerb Mathematik, 3
A square of sidelength $2^n$ is divided into unit squares. One of the unit squares is deleted. Prove that the rest of the square can be tiled with $L$-trominos.
combinatorics square trimino