Math 131

Spring 2000

This is due Friday, February 4 at the beginning of class. It is worth 10 points. Papers turned in before class on Monday lose 3 points; papers will not be accepted after Monday. Write neatly or use a word-processor. Your grade will depend on the correctness of your work and how well you explain it. You may discuss your work with me but not with others in the class.

Puzzle-solving is at the heart of mathematics, litigation and science. To prove or disprove a mathematical conjecture, you must piece together axioms and previous theorems in a precise way. To prosecute a case, you sift through the clues and legal precedents to construct a valid argument with the desired conclusion. To test a scientific theory, you must find a phenomenon predicted by the theory and construct an experiment that could disprove the theory.

You were asked to work exercise 38 on page 41 (there is a complete answer in the back of the book, although there are other ways to deduce the solution). In this assignment, we will start to explore how important each clue is to the overall solution. First, identify which of the original clues a-f is not needed to solve the case.

Change clue (a) to "There is only one murderer" (leave the other five clues the same). Solve the new mystery, explain your solution and discuss how much difference (if any) the change made.

Now, drop clue (a) altogether. Using clues b-f plus the one-cause-of-death assumption, can you eliminate anyone from suspicion? Indicate a couple of possibilities for murderer(s).