How many squares on a chessboard?
Number Theory
Level
2
How many squares of all sizes are there on a chessboard?
The answer is 204.
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1 solution
Assuming the chessboard is 8x8, we find that there are 64 squares of side 1, 49 of side 2, and in general n^2 squares of side 9 - n. Therefore the total number of squares is the sum of n^2 from n = 1 to n =8 = 8(9)(17)/6 = 204. Ed Gray