Question

Find the number of rectangles and squares in an 8 by 8 chess board respectively.

A 296, 204 Correct Answer Incorrect Answer
B 1092, 204 Correct Answer Incorrect Answer
C 204, 1092 Correct Answer Incorrect Answer
D 204, 1296 Correct Answer Incorrect Answer
E 1132,129 Correct Answer Incorrect Answer

Solution

Chess board consists of 9 horizontal 9 vertical lines. A rectangle can be formed by any two horizontal and two vertical lines. Number of rectangles = 9 C2  × 9 C2  = 1296. For squares there is one 8 by 8 square four 7 by 7 squares, nine 6 by 6 squares and like this number of squares on chess board = 12 +22 …..82  = 204 Only rectangles = 1296-204 = 1092

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