Welcome to Week 16 of the Wednesday Morning Math Challenge. You can find solutions to the Week 15 puzzle here, along with — more importantly — discussions of some ways to approach them. Remember that the real goal here is to think creatively.
This week, we’re going to deal with a seat assignment problem! Consider the following rather general problem:
Suppose that in a university department, there are k committees, each consisting of k faculty members, and that all committees meet in the same room, which has k chairs. Suppose also that at most one person belongs to the intersection of any two committees. Is it possible to assign the committee members to chairs in such a way that each member sits in the same chair for all the different committees to which he or she belongs?
- Is this the case for k=2?
- Can you show this for k=3?
- Is this possible for any choice of k?
Because this is the last week, solutions for this puzzle won’t be coming next week. If you can’t solve #3, don’t feel bad. It’s an open problem in mathematics! However, if you do solve #3, call me. It’s an open problem in mathematics!
I hope you’ve enjoyed this 16 week puzzle season as much as I did. What was your record over the stretch? Hopefully, you learned how to think in different and innovative ways, and carry this skills into your daily life.
Until next time,