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Topic: How many rectangles are in an n by n square array of dots?
Replies: 4   Last Post: Sep 9, 2006 11:14 PM

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Posts: 1,838
Registered: 12/6/04
Re: How many rectangles are in an n by n square array of dots?
Posted: Sep 9, 2006 1:35 AM
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On Sep 8, 2006, at 8:13 PM, Oliver Stemforn wrote:

> Let the n by n dots be in one plane, and let n be equal to or
> greater than 2. Rectangles here are understood to be squares or
> non-square rectangles. A rectangle counts only when each of its
> four vertices coincides with one of the dots of the array.***
> Can you come up with a polynomial in terms of n for the total
> number of rectangles for a general n by n array?

You are going to have to be more careful about when a rectangle
counts. Must the sides be horizontal/vertical? Or does the
rectangle formed by, say, (0,7), (4,10), (10,3), (6, 0) count when n
= 10? If so, the problem may be considerably more difficult than you

--Lou Talman
Department of Mathematical and Computer Sciences
Metropolitan State College of Denver


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