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# A 1-by-1 grid square contains 1 rectangle, and a 2-by-2 grid square contains 9 rectangles.

Going up further in size, 3-by-3 grid square contains 36 rectangles, and a 4-by-4 grid square contains 100 rectangles. How many rectangles are contained in a 5-by-5 grid square? Can you discover the formula, in terms of n, for the number of rectangles in an n-by-n grid square?

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69

### Best AnswerWarren(The Quiz Master) says

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4 years ago
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• TR Smith (calculus-geometry) 4 years ago

You got it first and with a great explanation. I'm glad no one attempted to count all 225 of them!

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82

### P Williams(paxwill) says

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4 years ago
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• TR Smith (calculus-geometry) 4 years ago

Very nice proof outline. You're right, the sum of the first n cube numbers is equivalent to the square of the nth triangular number, so that's another way to count the squares.

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61

### scottzozer says

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3 years ago
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• luchorin 3 years ago

see pasxwill's answer, it is the same combinatorial argument you mention.