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### Who Got Engaged to Whom?

```
Date: 11/27/2001 at 19:23:17
From: Alina Mergelova
Subject: Math mystery of the week

Young people: Dorothy, Jean, Virginia, Bill, Jim, and Tom became
engaged to one another (3 marriages to be). Who got engaged to whom?

- Tom who is older than Jim, is Dorothy's brother.
- Virginia is the oldest girl.
- The total age of each couple is the same, although no two people are
the same age.
- Jim and Jean together are as old as Bill and Dorothy.

Name the three pairs of engaged couples.

Thanks a lot.
```

```
Date: 11/30/2001 at 17:56:36
From: Doctor Barney
Subject: Re: Math mystery of the week

Tom cannot marry Dorothy, because he's her brother.

Tom cannot marry Virginia, either, because if he did, Jim (who is
younger than Tom) would have to marry someone older than Virginia for
their combined ages to be the same as Tom and Virginia's. But since
neither of the other young women is older than Virginia, Tom cannot
marry Virginia.

Therefore, Tom must marry Jean.

So who does Virginia marry? Suppose she marries Jim. IF Virginia
marries Jim, Dorothy must marry Bill (he's all that's left). BUT
Virginia and Jim's combined ages are more than Bill and Dorothy's
combined ages, because Bill and Dorothy are together the same as Jim
and Jean, and Virginia is older than Jean (she's the oldest girl).
Therefore, Virginia cannot marry Jim.

Virginia must marry Bill, and Dorothy will marry Jim.

If you write their names on a piece of paper, draw lines between them,
and make notes about their relationships, it helps. For example, I
drew a line between Tom and Dorothy and wrote "brother/sister" on the
line.

Have Fun!

- Doctor Barney, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Logic
High School Puzzles

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