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### Match Couples and Parties

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Date: 03/28/2001 at 20:14:16
From: Jesse
Subject: Logic problems

Five couples (Aston, Barler, Cauchy, Dick, Eggler) get together five
times a year (Halloween, Independence Day, New Year's Eve, St.
Patricks Day, Valentine's Day) for a party. Each couple hosts one of
the parties at their home (on Palmer, Quinton, Rawlins, Stoddard,
Talbot) and serves a different drink (coffee, fruit juice, iced tea,
lemonade, punch). The wives' first names are Freda, Ginny, Helene,
Ilene, and Julia. The husbands' first names are Kermit, Leon, Morton,
Norbert, and Orville. The party decorations, food, and costumes are
appropriate for each party.

Read the clues below and match everything up.

1. Mrs. Barler, Julia, and Ilene all shop at the same supermarket.
2. Everyone dressed in green for the party on Quinton.
3. Norbert and his wife picked up the Egglers and the couple that
served lemonade on their way to the Aston's party.
4. Helene and Freda both ask Mrs. Dick for the recipe for the
frosting on the heart-shaped cake she served at her party.
5. The couple on Stoddard decorated with pumpkins and served iced tea
at their party.
6. Orville told Mr. Eggler he should color the drink green at the
Eggler's party, but Mr. Eggler said his wife thinks it would look
unappetizing.
7. Ginny's husband made the coffee for their party while Ginny was on
the phone with Mrs. Cauchy.
8. Leon, Norbert, and Mr. Barler are all on the school board.
9. The couple on Palmer always look forward to going to the New
Year's Eve and Independence Day parties because they like to make
noise and stay up late.
10. Orville and his wife had a hard time finding confetti and
noisemakers for their last party because they waited too long to
go shopping.
11. The Rawlins couple were thinking about moving out of the city,
but Orville and the Barlers talked them our of it.
12. Neither Helene nor Kermit lives on Stoddard.
13. The Saint Patrick's Day party is not held at either of Kermit's or
Helene's houses.
14. The Cauchys and the couple on Talbot sometimes have dinner
together at a restaurant.
15. Helene does not live on Rawlins, and neither does Ilene.
16. Ginny is not married to Leon.
17. Fruit juice is not served at Orville's party.
```

```
Date: 03/30/2001 at 11:22:25
From: Doctor Rob
Subject: Re: Logic problems

Thanks for writing to Ask Dr. Math, Jesse.

Logic problems like these are pretty complicated, and often require
complicated analysis to derive the solution.

Your first task is to analyze all the statements to see what
conclusions are directly stated.  In this case, you can conclude the
following positive identifications, because they are stated in the
problem part indicated:

18. The St. Patrick's Day party was on Quinton Street. (#2)
19. The Dick family had the Valentine's Day party. (#4)
20. The Halloween party was on Stoddard Street. (#5)
21. Iced tea was served on Stoddard Street. (#5)
22. Iced tea was served at the Halloween party. (#5)
23. The Eggler family had the St. Patrick's Day party. (#6)
24. Orville was host of the New Year's Eve party. (#10)

Next, you can write down some negative statements, also from the
analysis of the problem parts above. For example,

25. Julia is not Mrs. Barler. (#1)
26. Ilene is not Mrs. Barler. (#1)
27. The St. Patrick's Day party was not on Palmer, Rawlins, Stoddard
or Talbot Streets; the Halloween, Independence Day, New Year's
Eve, and Valentine's Day parties were not on Quinton Street. (#2)
28. Norbert is not Mr. Eggler. (#3)
29. Norbert didn't serve lemonade. (#3)
30. Norbert isn't Mr. Aston. (#3)
31. The Eggler couple didn't serve lemonade. (#3)
32. The Aston couple didn't serve lemonade. (#3)
33. Helene is not Mrs. Dick. (#4)
34. Freda is not Mrs. Dick. (#4)
35. Helene was not hostess for the Valentine's Day party. (#4)
36. Freda was not hostess for the Valentine's Day party. (#4)
37. The Valentine's Day party was not hosted by the Aston, Barler,
Cauchy, or Eggler families; the Dick family did not host the
Halloween, Independence Day, New Year's Eve, or St. Patrick's Day
parties.
...
and so on.

Next, you can begin to draw some conclusions using the positive and
negative statements. For example, since Orville is not Mr. Barler
(#11), and Orville hosted the New Year's Day party (#24), you can see
that Mr. Barler did not host the New Year's Day party.

Then there is the process of elimination. For example, from #9, the
couple on Palmer Street did not host the New Year's Eve or
Independence Day parties. From #27, they did not host the St.
Patrick's Day party. From #5, they did not host the Halloween party.
Thus they must have hosted the Valentine's Day party. Then the
Valentine's Day party was not hosted by the couples on Quinton,
Rawlins, Stoddard, or Talbot Streets.

Using a combination of these techniques, and keeping careful track
of what you know (I use a 36-by-36 table), you can eventually
determine all the identifications.

I leave the rest of the fun to you!

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

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