Example 4.2.4 In an $8 \times 8$ chessboard, what is the minimum number of 
shapes that must be placed to achieve a saturated 
coverage (no additional shapes can be placed).
Solution: An $8 \times 8$ chessboard can be divided into 16 $2 \times 2$ squares. Each $2 \times 2$ square needs to cover at least 2 squares to possibly be saturated. Therefore, 16 $2 \times 2$ squares require at least 32 squares to be covered, which means at least 11 L-shaped pieces are needed. 11 L-shaped pieces can precisely form a saturated cover as shown in Figure 4-19.