# How Many Squares on a Chessboard? || Solution Explained

1 min readDec 8, 2020

Details : You are provided with a chessboard and are asked to find the number of squares in it. A chessboard is a board with 8 x 8 grids.

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**Solution: **Looking closely at the chessboard we can see that in addition to the 1 x 1 squares, there can be a combination of 2 x 2, 3 x 3, 4 x 4, 5 x 5, 6 x 6, 7 x 7, and 8 x 8 squares too. To get the total number of squares we need to find all the squares formed.

**1 x 1:** 8 * 8 = 64 squares.

**2 x 2:** 7 * 7 = 49 squares.

**3 x 3:** 6 * 6 = 36 squares.

**4 x 4:** 5 * 5 = 25 squares.

**5 x 5:** 4 * 4 = 16 squares.

**6 x 6:** 3 * 3 = 9 squares.

**7 x 7:** 2 * 2 = 4 squares.

**8 x 8:** 1 * 1 = 1 square.

Therefore, we have in all = 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 squares in a chessboard.