Homework. Due May 4.

1. Here is a typical ``logical'' puzzle (from http://www.pzzls.com/einsteins_riddle_puzzle.html, but try to do the puzzle without looking for the published solution):

   There are 5 houses in 5 different colors. In each house lives a person with a different nationality. The 5 owners drink a certain type of beverage, smoke a certain brand of cigar, and keep a certain pet. No owners have the same pet, smoke the same brand of cigar, or drink the same beverage.

   Somebody owns a fish. The question is: who?

   Hints:

   • The Brit lives in the red house.
   • The Swede keeps dogs as pets.
   • The Dane drinks tea.
   • The green house is on the left and next to the white house.
   • The green homeowner drinks coffee.
   • The person who smokes Pall Mall rears birds.
   • The owner of the yellow house smokes Dunhill.
   • The man living in the center house drinks milk.
   • The Norwegian lives in the first house.
   • The man who smokes Blends lives next to the one who keeps cats.
   • The man who keeps the horse lives next to the man who smokes Dunhill.
   • The owner who smokes Bluemaster drinks beer.
   • The German smokes Prince.
   • The Norwegian lives next to the blue house.
   • The man who smokes Blends has a neighbor who drinks water.

2. Here is another from the same source:

   A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony: There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

3. Here are two from "Logic Puzzles" (Brainden.com):

   You are in a room with no metal objects except for two iron rods. Only one of them is a magnet. How can you identify which one is a magnet?

4. There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position. How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?

5. Make up a mathematical puzzle of your own, along the lines of one of the ones we've seen this term, and bring it in to share with the class.