Let's have an 17x17 grid. We can fill this grid with 96 trominoes of three different colors, 32 trominoes of each color. On this particular grid the empty single square is the position A1. By visual inspection we see only 6 trominoes that do not form a pair (a pair is a 2x3 or3x2 rectangle); I marked these with red color. The rest of the trominoes form 45 pairs. Two trominoes of the same color are not allowed to touch anywhere side to side. Can you put the trominoes on this grid with only 10 pairs? You can put the empty single square anywhere on the grid.