CSCI 250 Spring 2012Discrete Structures Archived Class

# Homework 15

• Exercises taken from Discrete Mathematics and its Applications, Seventh Edition unless otherwise noted.
• You must show all of your work for each problem!
• Points will be deducted if you do not show all of your work.
• Each problem is generally worth 10 points. Problems with multiple parts may be assigned more points if there are enough parts or each part is significant enough.
• The Review Questions are always related to the section that will be discussed on the assignment due date.

## Details

SectionProblemNotes
1.410
2.338Your answer should be one or more equations that relate the constants (e.g. ab=c+d). An answer that gives an example of specific values of constants that work is not enough.
5.110It should be a very simple formula.
5.28Your answer should be something of the form "For \$5n, where n≥a" for some integer a (which you need to find). Then you will need strong induction to prove it. This is probably one of the more confusing problems, but look for the solutions of the similar ones in the book for some help.
10I will give you the answer to the first part: It is always n-1 breaks. For the inductive step, don't over think it. When you break the chocolate the first time, just make up sizes it breaks into (e.g. one piece will be size i (where i is at least 1), and the other then has to be what?). Strong induction makes this pretty straightforward.
30
32