Number of squares on a chessboard

♠ Posted by GeekyFry in , at 10:00 AM


How many squares are on a chess board?

Hint: If you thought it were 8×8 = 64. Think again ! Think about 2×2, 3×3,.. squares too :)




Possible Solution:

Let us break it down. 1×1 squares can be put on the chessboard in 8 horizontal and 8 vertical positions.
So total number of 1×1 squares = 8×8 = 64
Similarly 2×2 squares can be put on the chessboard in 7 horizontal and 7 vertical positions, making the number of 2×2 squares to be 7×7 = 49
We can extrapolate the above two result set to other dimension squares too:
1×1     8 x 8    = 64 squares
2×2     7 x 7   =  49 squares
3×3     6 x 6   = 36 squares
4×4     5 x 5   = 25 squares
5×5     4 x 4   = 16 squares
6×6     3 x 3   = 9 squares
7×7     2 x 2  = 4 squares
8×8     1×1     = 1 square

Total number of squares therefore =  64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 squares

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