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### Counting Rectangles

```
Date: 05/23/2001 at 08:34:36
From: Michael Calabrese
Subject: Columns and rows

Find the Rule:

Discover the rule for finding the number of different rectangles in a
square grid containing "c" columns and "r" rows.
get help from wherever we can.

Thanks,
Michael
```

```
Date: 05/23/2001 at 12:49:56
From: Doctor Peterson
Subject: Re: Columns and rows

Hi, Michael.

This is a fun problem, and I don't want to spoil it for you, so I'll
just give you a hint. Think about how you can choose a rectangle. You
can choose any pair of horizontal lines to make the top and bottom
rows of your rectangle, and you can choose any pair of vertical lines
to make the left and right columns. So to count all the rectangles you
can make, you first have to decide how many ways you can choose the
rows; then for each choice, you have the same number of ways to choose
the columns, so you can multiply.

If you haven't learned about Permutations and Combinations, you may
want to see the Dr. Math FAQ:

http://mathforum.org/dr.math/faq/faq.comb.perm.html

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Permutations and Combinations
High School Puzzles

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