**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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