Question 119
Given positive integers $m$ and $n \ge m$, determine the largest number of dominoes ($1 \times 2$ or $2 \times 1$ rectangles) that can be placed on a rectangular board with $m$ rows and $2n$ columns consisting of unit cells ($1 \times 1$ squares) so that:
1) each domino covers exactly two adjacent cells of the board;
2) no two dominoes overlap;
3) no two form a $2 \times 2$ square;
4) the bottom row of the board is completely covered by $n$ dominoes.
1) each domino covers exactly two adjacent cells of the board;
2) no two dominoes overlap;
3) no two form a $2 \times 2$ square;
4) the bottom row of the board is completely covered by $n$ dominoes.