CS2984: Introduction to Problem Solving
Homework Assignment 7

Due at 11:00pm on Tuesday, October 9
30 Points

See the General Guidelines for homework assignments. Note that submissions will not be graded that do not include the pledge statement available on the guidelines page.

This assignment may optionally be done with a partner. You are strongly advised to use a partner. If you do use a partner, then:

• The final submission should contain the name of both partners.
• Only one partner need actually make the submission to Web-CAT.
• Your solutions should explain, for each question, the contribution for each partner.

1. Here is another logic problem:

   Your company has five servers named Abe, Bob, Connie, Debby, and Ethan. At least one of these five servers has been compromised by a hacker. You've locked down the machines while your security team goes through the logs and file journals and discovers the following possibilities:

   • If Connie and Abe were compromised then Debby is compromised.
   • If Bob was compromised then Ethan was compromised.
   • If Debby and Connie were compromised then Ethan is safe
   • If Abe was compromised but Connie is safe then Debby is compromised.
   • If Debby was compromised then Connie was compromised.

   Your boss is pressuring you to find out which servers are safe so they can be put back on line. He complains that someone has already leaked information from Abe to the newspapers.

   Now that you know that Abe was compromised, can you pick out any servers that are safe? If so which ones. Justify your answer.

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).