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### Coat Confusion

```
Date: 03/20/98 at 07:40:23
From: David Maxwell
Subject: Logic

When the fire alarm went off 6 people in a room each grabbed a coat.

When they got outside, they found that no one had his own coat.

The coat A had belonged to the man who had seized B's.

The owner of the coat grabbed by C held a coat that belonged to the
man who was holding D's coat.

The man who seized E's coat was NOT the owner of the coat F grabbed.

a) Who has A's coat?
b) Whose coat does A have?
```

```
Date: 03/23/98 at 10:21:17
From: Doctor Sorelle
Subject: Re: Logic

Dear David,

I generally like to think of these types of problems in circles or
lines. I take a look at each of the clues and try to see a way to map
out what they are telling me.

The first clue in this problem says that the coat A now has belongs
to an unknown man who is holding B's coat. I can represent that by:

A -> __ -> B

meaning A has the coat of someone who has B's coat.

The next clue is a little more confusing.

C grabbed the coat of the man who was holding the coat belonging to
the man holding D's coat... hmmm... so in this clue there are two
unknown people in the chain, the man whose coat C is holding and the
man holding D's coat. The chain I now make looks like this:

C -> __ -> __ -> D

Then the last clue: F did not grab the coat of the man who has E's
coat. I represented that as:

This is NOT true:
F -> __ -> E

Now I try to combine the chains into one long chain or a couple of
smaller ones. Maybe the first two chains can go into the big chain:

A -> C -> B -> __ -> D -> __ -> A (it's like a circle)

That seems to work as far as the first two clues go, but what about
the third?  Can you see where the E and the F would go?  Now do you
think that you can answer the questions?

Have fun!

-Doctor Sorelle,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/
```

```
Date: 03/25/98 at 09:30:31
From: Youngho Cho
Subject: Re: Logic

Couldn't you "link" the chains in different ways to produce different
results?

e.g. C -> F -> A -> D -> B -> E -> A

Please help.

Thanks.
```

```
Date: 03/27/98 at 09:29:42
From: Doctor Sorelle
Subject: Re: Logic

David,

Yes, it does seem to me that you could link the chains in different
ways to produce different results. I found one other way of linking
them:

C -> F -> A -> D -> B -> E -> C

which is the same as the other one that you found, except instead of
having an A at the end of my chain I have a C. You used A twice
(oops!).

What I think is interesting is that both times the same person is
holding A's coat!

The two different ways do produce two different answers to the
question of whose coat A is holding. But don't worry about it, it's
okay to have two different answers to the same question, as long as
they both make sense!

:-)

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

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