To solve the problem (assuming it refers to the number of ways to tile a 2×10 rectangle with 1×2 dominoes), we use the Fibonacci sequence.

Key Observations:

• The number of ways to tile a 2×n rectangle follows the Fibonacci sequence. Let (f(n)) denote the number of ways:
  • (f(1) = 1) (one vertical domino),
  • (f(2) = 2) (two vertical or two horizontal dominoes),
  • For (n \geq 3), (f(n) = f(n-1) + f(n-2)) (add a vertical domino to a 2×(n-1) tiling, or two horizontal dominoes to a 2×(n-2) tiling).

Calculations:

(f(3) = f(2) + f(1) = 2 + 1 = 3)
(f(4) = f(3) + f(2) = 3 + 2 = 5)
(f(5) = 5 + 3 = 8)
(f(6) = 8 + 5 = 13)
(f(7) = 13 + 8 = 21)
(f(8) = 21 + 13 = 34)
(f(9) = 34 + 21 = 55)
(f(10) = 55 + 34 = 89)

Answer: (\boxed{89})

作者声明:本文包含人工智能生成内容。