Match Couples and Parties
Date: 03/28/2001 at 20:14:16 From: Jesse Subject: Logic problems Please help me solve this logic problem: 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/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994-2013 The Math Forum