Discrete Math - Day 9

I started class with three pigeon-hole problems. I asked students to work on these on their own as this would be a good assessment for them as to how well they understood these types of problems. The first two problems were relatively straight-forward: 1) How many people do you need in a room to guarantee that at least two people were born on the same day of the week? and 2) How many people do you need in a room to guarantee that at least two people were born in the same month? Students did very well on these problems.

The third problem was a slight variation on the first question: How many people do you need in a room to guarantee that at least two people were born on Monday? It was interesting to hear how many students were troubled by this question. A few were able to articulate the troubling issue and why it was conceivable that you would never have this situation occur no matter how many people were in the room. As someone said, "No one likes Mondays."

I then had students consider the problems and what characteristics made the pigeon-hole principle applicable or not.

We then took on a more challenging counting problem. In fact, the next series of problems that we'll work on came from an article in the February, 2010 issue of Mathematics Teacher entitled "Common Errors in Counting Problems." This article provides a series of challenging problems that delve into the complexity of counting problems at an accessible level for students.

The first problem involves determining the number of possible flags that can be formed if a flag has eight horizontal stripes of colors red, green, or blue, and the flag must contain at least six blue stripes. Students worked on this problem for the rest of the period. There