Question

Find the number of rectangles in 8×8 chessboard. (not just the 1x1 squares)

Answer 1

288

Explanation:

Number of rectangles

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1 × 1 squares 9-1 = 1 = 8*8 = 64

1 × 2 squares 9-2 = 7 = 8*7 = 56

1 × 3 squares 9-3 = 6 = 8*6 = 48

1 × 4 squares 9-4 = 5 = 8*5 = 40

1 × 5 squares 9-5 = 4 = 8*4 =32

1 × 6 squares 9-6 = 3 = 8*3 = 24

1 × 7 squares 9-7 = 2 = 8*2 = 16

1 × 8 squares 9-8 = 1 = 8*1 = 8

64 + 56 + 48 + 40 + 32 + 24 + 16 + 8 = 288

Thus,

the number of squares on a chessboard is 228.

Hope this helps :)