Associated Topics || Dr. Math Home || Search Dr. Math

### 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
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Word Problems

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search