How many squares are on a chessboard?

How to get close to this number

Eight by eight, multiplied. The board is a square grid whose side length everybody knows, so the answer is a single multiplication — and rebuilding it from the grid is faster and safer than recalling the product.

A pedantic reading gives a much larger answer, and it is worth knowing: if you count squares of every size, from one by one up to eight by eight, the total is the sum of the squares from one to sixty-four, which comes to two hundred and four. The question as asked means the playing squares, but the puzzle version of it is a classic.

The checkers detail in the explanation is the neat structural fact: the same board serves a game that uses only half of it. Thirty-two squares sit unused for an entire game of draughts, because pieces move diagonally and therefore never leave their colour. Two games share a physical object while occupying different halves of it.