Question 85
Let $a$ and $b$ be odd natural numbers greater than 1. Consider an $a \times b$ board from which the cells $(2,1),(a-2, b)$ and $(a, b)$ are missing (by the cell $(i, j)$ we mean the cell at the intersection of row $i$ and column $j$). Suppose that such a board is tiled with $2 \times 1$ dominoes and $2 \times 2$ squares (the dominoes may be rotated).
Prove that at least $\frac{3}{2}(a+b)-6$ dominoes are used. (Nikola Petrović)
Prove that at least $\frac{3}{2}(a+b)-6$ dominoes are used. (Nikola Petrović)