Question

How many squares are on an 8x8 chessboard? (The answer is not 64)

Answer 1

don't you have to do 8*8*8*8?

Answer 2

64: 1x1 squares
... 2x2 squares
... 3x3 squares
... 4x4 squares
... 5x5 squares
9 6x6 squares
4: 7x7 squares
1: 8x8 squares

Total squares = 64 + ... + ... + ... + ... +9 + 4 + 1 =

Answer 3

notice a pattern forming?

Answer 4

\[T =\sum_{i=1}^8i^2\]

Answer 5

The answer is equal to the eighth square pyramid number. Easy: 64 1x1, 49 2x2, 36 3x3, 25 4x4, 16 5x5, 9 6x6, 4 7x7 and 1 8x8. Total 204 squares. There are 204 squares in a 8x8 chess board.