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How many rectangles of all sizes, squares included, can be drawn along the lines of an $8 \times 8$ chessboard?

Competition practicePermutations & Combinations

A204
B1296
C784
D1024

Step-by-Step Solution

A rectangle is fixed by 2 of the 9 vertical lines and 2 of the 9 horizontal lines:

^{9} C_{2} \times^{9} C_{2} = 36 \times 36 = 1296

. (204 counts only the squares.)

Answer: B) 1296

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