CATEGORICAL FUN

Introduction
1. The Singles Bar
2. Not Entirely Identical Twins
3. The Flower Show
4. The Dorms
5. Class Reports
6. Downtown Portland

Introduction

The following are logical problems, or "brain-teasers," which contain the information needed for their solutions, but present it in indirect but relational ways. Consider the following relational statements: From this, of course, we can conclude that the red book belongs to Ivan, but it takes three bits of information to link "red book" and "Ivan." Each statement establishes relationships by creating or limiting a category. "The red book belongs to Ludmilla's brother," for instance, shows that the owner of the book falls into the category of "brothers of Ludmilla." The second statement gives us one member of that category, and the third statement limits the category to that one member. This example is simple enough that you probably were not conscious of the categorical thinking you employed in solving it, but the greater complexity of the following problems makes it important to attack them step by step, category by category.

Assignment: Keep a written record, or journal, of how you approach and solve each of the following problems. Be specific about what categories you are establishing, and why something fits into one category and can be excluded from another.


1. The Singles Bar

While sitting in a club where all single men tell the truth and all married men lie, a woman is approached by three men. She asks the first guy if he is married, but the music is so loud that she can't hear his answer. So she turns to the second guy, who tells her, "The first guy said, 'I am married,' but he really is single." Then she turns to the third guy, who says, "The second guy is single." Determine the marital status of each of the three men.

2. Not Entirely Identical Twins

A man is sitting with two women, seemingly identical twins. One of the women always tells the truth, the other always lies, but the man does not know which one is which. The women have served him a pair of drinks, one of which contains a tasteless, odorless, but deadly poison, the other the cure for a fatal disease he has contracted. Before choosing which glass to drink, the man may ask one question of one of the women. Can you formulate a question that would guarantee the safety of the drink chosen?

3. The Flower Show

Jasmine, Rose, and Lily each had an entry in the county fair's flower competition. Coincidentally, the flowers they entered were a jasmine, a rose, and a lily, but not in that order--in fact, none of the three competitors entered her namesake flower. If, in addition, you know that Jasmine did not enter a rose, can you figure out which flower each woman entered?

4. The Dorms

Three women--named Dana, Alex, and Jean, all Business majors--signed up for a critical thinking class at San Jose State at the same time as three men--also named Dana, Alex, and Jean--did. The three men are majoring in English, Engineering, and Nursing, though not necessarily in that order. Given the following information, can you assign the correct name to each of those majors?
  1. Jean lives in San Francisco with her mother.
  2. The Engineering major lives on the peninsula, exactly halfway between San Jose and San Francisco.
  3. Alex is joined in studying at San Jose State by both of her brothers.
  4. The woman who lives nearest the Engineering major has three times as many brothers as he does.
  5. The women with the same name as the Engineering major lives in San Jose.
  6. Dana says he is smarter than the English major.

5. Class Reports

Five students in the Hebrew literature course (Dror, Hava, Eitan, Maya, and Zvike) have been assigned reports on five modern Hebrew writers (Oz, Agnon, Rahel, Yehoshua, and Bialik). Each student has a different writer, and each report will be made on a different day of the week (Sunday, Monday, Tuesday, Wednesday, or Thursday). From the following information, determine which student will be reporting on which day about which author:
  1. The report on Agnon will be given on Monday, and the report on Oz will be given on Wednesday, but the report on Rahel will not be given on Thursday, and the report on Bialik will not be given on either Sunday or Thursday.
  2. Neither Zvike nor Dror nor Maya is doing the report on Yehoshua, but Eitan is doing the report on Rahel.
  3. Zvike is not giving his report on Monday, and Dror is not giving his report on either Monday or Wednesday.

6. Downtown Portland

In downtown Portland, the streets running east and west are named alphabetically (Ankeny, Burnside, Couch, Davis, and Everett Streets), and those running north and south are numbered (1st, 2nd, 3rd, 4th, and 5th Avenues). At each of the twenty-five intersections where those streets meet, the city limits the number of newspapers sold and the number of buses that stop to just one. Plot out which newspaper and which bus is at which intersection from the following information:

  1. There are seven newspapers (The Oregonian, Oregon Journal, Portland Reporter, Journal of Commerce, Willamette Week, The Bridge, and Nickel Ads), and seven buses (routes 14, 17, 23, 27, 42, 64, 68).
  2. No newspaper or bus can be found more than once on any street. Nor can they be duplicated along the imaginary diagonals of the area (1st & Ankeny to 5th & Everett, and 1st & Everett to 5th & Ankeny).
  3. No two intersections have exactly the same combination of newspaper and bus.
  4. The 14 bus stops at 3rd & Everett, and has fewer than five stops total.
  5. The 17 bus stops at 2nd & Burnside.
  6. The 23 bus stops at 2nd & Davis.
  7. The 42 bus stops at 1st & Couch
  8. The 64 bus stops at 4th & Burnside.
  9. The 68 bus stops at 5th & Davis.
  10. Nickel Ads is sold at 4th & Ankeny.
  11. The Oregonian is sold at 1st & Davis.
  12. The Portland Reporter is sold at 5th & Burnside.
  13. The same bus stops at 2nd & Couch and the intersection on Davis that has the Oregon Journal.
  14. The same bus stops at 3rd & Couch, 5th & Burnside, and one intersection with The Bridge, but not at 2nd & Everett.
  15. The same bus stops at 1st & Burnside and 3rd & Ankeny.
  16. The same bus stops at 4th & Davis and 3rd & Burnside.
  17. The same bus stops at 2nd & Ankeny and 4th & Couch.
  18. The same bus stops at 1st & Davis and the intersection on 2nd that has Willamette Week.
  19. Different buses stop at 1st & Everett and 2nd & Couch
  20. Different buses stop at 4th & Davis and 5th & Ankeny.
  21. Different newspapers are sold at 2nd & Everett and 5th and Davis.
  22. Different newspapers are sold at 3rd & Davis and 5th & Ankeny.
  23. Different newspapers are sold at 1st & Burnside and 3rd & Couch.
  24. Different newspapers are sold at 4th & Couch and 5th & Everett.
  25. The same newspaper is sold at 1st & Ankeny and 5th & Couch.
  26. The same newspaper is sold at 2nd & Couch and 4th & Everett.
  27. The Oregonian is not sold at 5th & Everett.
  28. One intersection has the 23 bus and the Oregonian.