Daily Math Puzzle #3 'How Many Squares and Rectangles are On a Chessboard?'

[@bp56789]

How many rectangles = Choose two unordered squares with replacement = {64+2-1 \choose 2} = 2080. Or equivalently, {64 \choose 2} + {64 \choose 1} = 2080. Hmm, different from your answer. But your reasoning seem correct too. Any tips on where I went wrong?

[@bp56789]

Ah, I got it. I double counted the rectangles that were 2x2 or larger because there are two ways to define the corners.

[@witzar]

Another way to count rectangles: 1^3 + 2^3 + ... + 8^3.