【Question 16】  
Use 9 pieces of $2 \times 1$ rectangular paper to cover a $2 \times 9$ chessboard. There are $\qquad$ different ways.
【Analysis and Solution】
$2 \times 1$ chessboard has 1 way;
$2 \times 2$ chessboard has 2 ways;
For $n \times 2$ chessboard $(n \geqslant 3)$
If a $2 \times 1$ rectangle is placed vertically in the first row, then the number of ways is the same as for $(n-1) \times 2$;

If two $1 \times 2$ rectangles are placed horizontally in the first and second rows, then the number of ways is the same as for $(n-2) \times 2$;
$2 \times 3$ chessboard has $1+2=3$ ways;
$2 \times 4$ chessboard has $2+3=5$ ways;
$2 \times 5$ chessboard has $3+5=8$ ways;
$2 \times 6$ chessboard has $5+8=13$ ways;
$2 \times 7$ chessboard has $8+13=21$ ways;
$2 \times 8$ chessboard has $13+21=34$ ways;
$2 \times 9$ chessboard has $21+34=55$ ways;