← The Arithmetic of the Chessboard · Lesson 3 of 3
How many squares
A chessboard has 64 small squares, but count every square of every size and there are many more: 1 × 1, 2 × 2, all the way up to the whole board.
A k × k square fits in (9 − k) positions across and (9 − k) down. Adding up 8² + 7² + … + 1² gives 204.
On a 4 × 4 board, how many squares are there of every size?
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