Laying a Brick Walkway
Date: 04/22/2002 at 09:25:38 From: Dawn Subject: Math Word Problem I have to build a walkway, 2ft. by 20ft., out of bricks that are 1ft. by 2ft. The bricks can lie vertically and horizontally but in no other direction. How many different ways can I build this walkway? I know there has to be a pattern, but I do not see it. Any help would be great. Dawn
Date: 04/22/2002 at 12:30:51 From: Doctor Peterson Subject: Re: Math Word Problem Hi, Dawn. When I don't see how to solve a problem like this, I start by playing with the ideas involved in the problem. That usually means simplifying the problem by working with smaller, easier numbers - actually, that's more or less what children's play is, isn't it? By trying things out in a smaller case, I get a feel for how it works. And in this case, that leads directly to a solution. How many ways can you make a 2-by-1 walkway (silly as it sounds!)? One, of course: | | How about a 2-by-2 walkway? Two ways: | | --- | | --- How about 2-by-3? You can build on what you have already done: if the first brick you place is vertical (across the walk), you have 2 more feet to fill in, using one of the solutions for the 2-by-2. What happens if the first brick is horizontal (lengthwise)? See if you can use this to identify a pattern. You will recognize a relationship to the Fibonacci sequence, which you can read about in the Dr. Math FAQ: Golden Ratio, Fibonacci Sequence http://mathforum.org/dr.math/faq/faq.golden.ratio.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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