Counting RectanglesDate: 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/ |
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