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/