The insight: each domino covers exactly 2 cells. The board has cells total. So the maximum number of dominoes is (M × N) / 2. You're dividing the total area by the domino size.
Wait, but what about odd areas? If , you can't place dominoes. That's where integer division comes in. Floor division (M × N) / 2 gives you the answer, automatically handling the leftover cell.
You don't need to simulate placement. No loops, no complex logic. Just multiply the dimensions and divide by 2. This transforms a geometric problem into a single arithmetic operation.