How would you find the number of squares on a chessboard?
let’s take a 3×3 square as an example: the 3×3 square can be in 6 positions horizontally and 6 positions vertically, giving a total of 6*6 = 36 3×3 squares on the chessboard.
Number of squares for an NxN chessboard?
n2 + (n-1)2 + (n-2)2 + …. (1)2.
It is actually equal to n(n + 1)(2n + 1)/6
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let’s take a 3×3 square as an example: the 3×3 square can be in 6 positions horizontally and 6 positions vertically, giving a total of 6*6 = 36 3×3 squares on the chessboard.
| Square Size | Total Appearances on Board |
| 1×1 | 64 |
| 2×2 | 49 |
| 3×3 | 36 |
| 4×4 | 25 |
| 5×5 | 16 |
| 6×6 | 9 |
| 7×7 | 4 |
| 8×8 | 1 |
| TOTAL | 204 |
Number of squares for an NxN chessboard?
n2 + (n-1)2 + (n-2)2 + …. (1)2.
It is actually equal to n(n + 1)(2n + 1)/6
Read full article from Find number of squares chessboard
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