How many squares of all sizes can be found on a large square made of 10000 small squares? I don't want to try them out or count them. I tried finding a pattern, as in a square made of 1^2 small square has 1 square of all sizes, a square made of 2^2 squares has 5, a square of 3^2 has 14, etc. There is a pattern of adding the squares of consecutive numbers starting at one, but I don't want to add all the way up to 100. Is there a better way?
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$\begingroup$ Yes, use the formula for the sum of first n squares: n(n+1)(2n+1)/6. Thus I'm voting to close this question because there is nothing puzzly going on about it. $\endgroup$– BubblerCommented Jul 3 at 2:33
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$\begingroup$ Welcome to PSE (Puzzling Stack Exchange)! $\endgroup$– Will.Octagon.GibsonCommented Jul 3 at 3:32
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$\begingroup$ You can find information about summing the first n squares here: math.stackexchange.com/questions/48080/… $\endgroup$– Will.Octagon.GibsonCommented Jul 3 at 3:38
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