Number of squares in a chessboard

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Number of squares in a chessboard

As you know, a chessboard consists of 8 by 8 litle squares. Can you tell how many total squares you can find on the board? including 2 by 2, 3 by 3, 4 by 4, 5 by 5, 6 by 6, 7 by 7 and 8 by 8 squares?

Posted 194 day ago

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Answers (1)

Catherine

Σ(n=1 to 8)n^2 = 204

Squares of size 1x1 = 8²
Squares of size 2x2 = 7²
Squares of size 3x3 = 6²
...
Squares of size 8x8 = 1²

If you want a visualization to this pattern take a square say 5x5,
look at how many files you can position it horizontally on the board (4) and how many ranks you can position it vertically on the board (4). If you multiply these two numbers it will give you the number of distinct positions for that size square (16).

Posted 193 day ago

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