MathDB

On a

100 \times 100

chessboard, the plan is to place several

1 \times 3

boards and

3 \times 1

board, so that
[*] 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.
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)

.
Proposed by Muhammad Afifurrahman, Indonesia

Problem Statement