Domineering games with minimal number of moves

Rohan Karthikeyan, Siddharth Sinha

Published 2020-05-06Version 1

Domineering is a two-player game played on a checkerboard in which one player places dominoes vertically, while the other places them horizontally. In this paper, we find out the minimum number of moves for a game of Domineering to end on several rectangular $m \times n$ boards. We also formulate two conjectures pertaining to $2 \times n$ (similarly $m \times 2$) and on $3 \times n$ (similarly, $m \times 3$) boards.