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How Many Pencils?


Date: 9/11/96 at 20:41:54
From: Anonymous
Subject: How Many Pencils?

Al is an artist who uses color pencils to sketch.  How many pencils 
does Al have if all of them are blue except two, all of them are 
yellow except two, and all of them are red except two?


Date: 9/11/96 at 21:56:50
From: Doctor Patrick
Subject: Re: How Many Pencils?

Hi!  First, let me ask you a question - how many different colors 
does Al have?  

You should see that he has three colors.  This means that if all of 
them are blue except for two, then the two that are left must be the 
red and the yellow.  

This means that there is one red and one yellow, but we don't know how 
many blues there are.  If we look at the next statement, which says 
that all of them are red except for two, and there are two colors 
left, we again know that the two left must be for the two colors which 
are also left - one each.  This gives us one blue, and, again, one 
yellow.  

Now we know that there is one blue, one yellow and one red.  With no 
other colors, this adds up to three colored pencils.

-Doctor Patrick,  The Math Forum
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