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### Baseball Game Logic Puzzle

```Date: 10/23/2006 at 11:24:27
From: Deidre
Subject: Baseball Games

One day, four baseball games were played.  The teams that played in
those games were the Braves, Cardinals, Cubs, Dodgers, Giants, Mets,
Pirates, and Reds.  May, Kay, and Ray picked the teams that they
thought would be the winners of those games.  The choices for each
person are as follows:

May:  Braves, Cubs, Giants, Pirates

Kay:  Cubs, Dodgers, Pirates, Reds

Ray:  Cardinals, Giants, Pirates, Reds

Determine which teams played which other teams.  List the four games
according to the teams that played.

```

```
Date: 10/23/2006 at 13:40:56
From: Doctor Douglas
Subject: Re: Baseball Games

Hi Deidre.

I'll get you started.  Since May's picks are all from different
games, we can fill in the schedule of games as follows:

Braves   vs    ?
Cubs     vs    ?        This table encapsulates all the
Giants   vs    ?        information we have from May.
Pirates  vs    ?

Now consider Kay's picks.  We see Cubs and Pirates, but Dodgers and
Reds must be teams from the right hand side of the schedule.  Neither
the Dodgers nor the Reds can play the Cubs or the Pirates, because Kay
picked all four of these teams to win from different games.  Thus, by
incorporating Kay's picks, the schedule must look like either of the
following:

Braves   vs    Dodgers?           Braves  vs    Reds?
Cubs     vs       ?       -OR-    Cubs    vs      ?
Giants   vs     Reds?             Giants  vs   Dodgers?
Pirates  vs       ?               Pirates vs      ?

Now use Ray's picks to figure out which of these two schedules is
correct, and how to complete it.

I hope that this helps.  Please write back if you have further

- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/
```
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