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### Math Logic

```
Date: 6/5/96 at 9:32:19
From: Jim Marone
Subject: Math logic

This is a problem about logic.

Sally, Ron, Jim, and Meghan are President, VP, Treasurer, and Captain
of the cheerleading squad, but not necessarily in that order. Who is
what?

Clues

Sally loves money.
Meghan thinks she could not handle a whole class
Jim was elected
Ron is Jim's partner
```

```
Date: 6/14/96 at 0:49:40
From: Doctor Jeffrey
Subject: Re: math logic

Sally    Treasurer
Ron      Vice President
Jim      President
Meghan   Captain

This is how I got it:

The first thing I did was make a chart (they usualy help with logic
problems). The chart I made had the names in the rows and the
positions in the columns. If I know that someone has a certain
position, I put an o in that part of the chart. If I know that someone
doesn't hold a certain position, I put an x there. This is the chart I
started with:

P     V     T     C
-------------------------
S |     |     |     |     |
-------------------------
R |     |     |     |     |
-------------------------
J |     |     |     |     |
-------------------------
M |     |     |     |     |
-------------------------

From this point I started using the clues.  The first clue I used was
the fact that Meghan wouldn't have gone for President since she didn't
want to lead the whole class. After using this piece of information,
the chart looks like this:

P     V     T     C
-------------------------
S |     |     |     |     |
-------------------------
R |     |     |     |     |
-------------------------
J |     |     |     |     |
-------------------------
M |  x  |     |     |     |
-------------------------

Next, since Sally loves money, she was probably the Treasurer.

P     V     T     C
-------------------------
S |  x  |  x  |  o  |  x  |
-------------------------
R |     |     |  x  |     |
-------------------------
J |     |     |  x  |     |
-------------------------
M |  x  |     |  x  |     |
-------------------------

I was able to fill in the additional x's because I know Sally can only
hold one position and only one person can be treasurer.

Since Ron and Jim are partners they had better be the President and
Vice President, so Meghan must be the Captain.  So now it looks like
this:

P     V     T     C
-------------------------
S |  x  |  x  |  o  |  x  |
-------------------------
R |     |     |  x  |  x  |
-------------------------
J |     |     |  x  |  x  |
-------------------------
M |  x  |  x  |  x  |  o  |
-------------------------

This leaves President and Vice President for Ron and Jim.  Since
Presidents are elected and Vice Presidents are not, Jim must be
President and Ron must be Vice President.

-Doctor Jeffrey,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Word Problems
High School Logic
Middle School Logic
Middle School Word Problems

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