How many squares ?

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are there in total ?

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They all look like rectangles to me .

Alan

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ok, how many squares (or rectangles, depending on your browser settings) are there ?

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none? they all only have 2 sides?

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none? they all only have 2 sides?

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ok, how many squares (or rectangles, depending on your browser settings) are there ?

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They all look like rectangles to me .

Alan

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There are 12*12 squares of size 1 by 1, 11*11 squares of size 2 by 2, etc. So the total number is

12*12 + 11*11 + … + 2*2 + 1*1 = 650

The general formula for an n by n grid is n*(n+1)*(2*n+1)/6

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while you got the correct result, I think it’s a lot simpler to use this formula: (1² + 2² + 3² … + 12²)

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That’s basically what I had, but how are you going to compute that quickly for, say, a 50 by 50 grid?

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That’s basically what I had, but how are you going to compute that quickly for, say, a 50 by 50 grid?

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while you got the correct result, I think it’s a lot simpler to use this formula: (1² + 2² + 3² … + 12²)

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There are 12*12 squares of size 1 by 1, 11*11 squares of size 2 by 2, etc. So the total number is

12*12 + 11*11 + … + 2*2 + 1*1 = 650

The general formula for an n by n grid is n*(n+1)*(2*n+1)/6

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If you are wanting total SQUARES then…
12*12 + 6*6 + 4*3 + 1 = 193

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If you are wanting total SQUARES then…
12*12 + 6*6 + 4*3 + 1 = 193

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