Math 160 Mathematical Problems and Games, Fall 2002
Problem Set 6: hand in one problem Tuesday, October 29.

As always, think about all four problems.  Then choose one to write up and hand in.

Knights and Knaves.  On a certain island, all of the inhabitants are either "knights," who always tell the truth, or "knaves," who always lie.  Warmup questions:  a) If you ask an islander, "Are you a knight or a knave?" what will they say?  b)  If you meet a person on this island who says, "I am a knave," are they an islander or a visitor?

1.  On your way to the island's ice cream stand, you encounter a fork in the road.  You know that the ice cream stand is either to the left or to the right, but you can't remember which.  You stop a passing islander to ask directions, but she is in a hurry and only has time to answer one question.  You're not sure whether she is a knight or a knave.  What one question can you ask her to find the way to the ice cream stand?

2.  You are introduced to three people on the island, Alicia, Bernice, and Carl.  You know that one is a knight, one is a knave, and one is a visitor to the island, who sometimes lies and sometimes tells the truth.  During your conversation, Alicia tells you that she is a visitor.  Bernice tells you that Alicia and Carl sometimes tell the truth.  And Carl tells you that Bernice is a visitor.  Who is who?

3.  There are five houses in a row (west to east), each of a different color and inhabited by people of different nationalities, with different pets, driving different automobiles, and enjoying different beverages.

1. The English family lives in the red house.
2. The Spanish family drives the Prism.
3. Espresso is drunk in the green house.
4. The Ukrainians drink iced tea with lemon.
5. The green house is immediately east of the white house.
6. The family who owns the gerbil drives the Saturn.
7. The cat owners live in the yellow house.
8. Skim milk is drunk in the middle house.
9. The Norwegian family lives in the most westerly house.
10. The dog owners live next to the people who drive the Miata.
11. The cat lives in the house next to the people who drive the Corvette.
12. The pony owners drink grapefruit juice cocktail.
13. The Japanese family owns a chimpanzee.
14. The Norwegian family lives next to the blue house.

Who drinks the hot chocolate?  And who owns the Infiniti?

4.  On Wednesday, May 8, the wicked Simon Legrew was murdered at his home near Boston.  The police were able to place the time of death at between 11:10 and 11:30 pm.  They arrested four suspects:  Jeeves, the butler; Fifi, the French maid; Julia, the cook; and Jessica, Mr. Legrew's private secretary.  Under questioning, the four suspects made the following statements.

    Jeeves:  I didn't do it.  Jessica did it.  Mr. Legrew was blackmailing Jessica.  Fifi and I were watching television together from 10:10 pm until 12:30 am.
    Fifi:  I'm innocent.  Jeeves and I were watching television together at the time of the murder.  Jessica was being blackmailed.  I saw Jessica speaking to Mr. Legrew at 9:30pm on the night of the murder.
    Julia:  I'm innocent.  Jessica was being blackmailed.  Jeeves murdered Mr. Legrew.  I saw Jessica leave the house at 10:00 pm.
    Jessica:  I do not kill Mr. Legrew.  I was not being blackmailed.  I was in Chicago during the entire night of the murder.  Fifi is the murderess.

Each of the suspects made two true statements and told two lies.  Who murdered Mr. Legrew?