A 2 × n rectangular board has black and white squares in a checkerboard pattern. Prove by induction on n that if one white square and one black square are removed, then the rest of the squares be tiled by 2 × 1 or 1 × 2 dominoes. (Hint: Case analysis can help.)
Figure 1: A general 2 × n checkerboard (left), and a 2 × 5 checkerboard with one white and one black square removed, tiled by 2 × 1 and 1 × 2 dominoes (right).