Hint #27: Number of Squares on a Chessboard
Lets first establish what we mean by a square to be clear why the answer is not 64. Below are some examples of valid squares.
The method I used was to think about a square of a specific size say a 2x2. And consider the number of locations that square can go. There is a simple relationship between the size of a square and the number of locations it can be placed.
Moving on to rectangles the same technique can still be used. Although it's a lot more fiddly. A better solution involves counting the number of available diagonals.
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