CS2984: Introduction to Problem Solving
Homework Assignment 8 Problems

Due at 11:00pm on Tuesday, March 18
30 Points

Don't forget to include the pledge statement!

  1. Here is another logic problem. In this problem, the statement "If A then B" means that when A is true, we know that B is true as well. However, if A is not true, this statement tells us nothing about the truth of B.

    Culinary anthropologist Margaret Smith is trying to reconstruct the recipe for a special fruit salad traditionally prepared by the Natanese people. Through extensive research, she has discovered the following clues about the fruit salad.

    1. If apples are in the salad or bananas are in the salad, then cherries are not in the salad.
    2. If plums are in the salad or oranges are in the salad, then lemons are in the salad.
    3. If grapes are not in the salad, then plums are in the salad.
    4. If oranges are in the salad and bananas are in the salad, then apples are not in the salad.
    5. If plums are not in the salad, then oranges are in the salad.
    6. If lemons are in the salad, then bananas are in the salad.
    7. If cherries are not in the salad, then oranges are in the salad.
    8. If bananas are in the salad and cherries are in the salad, then apples are in the salad.
    9. If bananas are not in the salad and cherries are in the salad, then lemons are in the salad.
    10. If bananas are not in the salad, then either plums are in the salad or oranges are in the salad.
    11. If oranges are in the salad, then grapes are not in the salad.

    Exactly which fruits are in the salad? Explain how you arrived logically at your conclusion.

  2. Reconsider the solution given for the Handshaking problem presented in the book and in class. Present a new solution explanation to the problem that is based on the heuristic of simplification.

  3. Create a cryptoarithmetic problem of your own. Here are the requirements:
    • Create an addition problem with either two or three numbers being added.
    • There must be at least 11 digits among the numbers being added (this does not count the number of digits in the solution). For example, the last homework assignment's problem #1 had 9 digits (plus 4 digits in the solution).
    • All of the values being added, and the solution, must be coded by commonly known words or names.
    • The solution must be a correct addition.
    • There can be only one correct assignment of digits to letters to solve the problem.
    • This problem must be original (the grader must not be able to find it in any online repository or website, nor can it be a trivial derivative of a known problem in any online repository or website).
    • Once you have your cryptoarithmetic problem, show a solution. That is, give a plausible series of steps that leads from your problem to the unique solution.