## 187 – Some extra credit problems

I have extended the deadline for extra credit problems: They are now due at the beginning of the final exam. In addition to the previous problems, I will be adding a few more through the next few days in this post.

• The problem at the end of the second midterm. Specifically, find (with proof) the correct formula for the resulting number of regions, when $n$ points are positioned on the circumference of a circle, and all possible lines between them are drawn. This problem is due to Leo Moser and is discussed in a few places, for example, in Mathematical Circus, by Martin Gardner.
• Given $n+1$ numbers from $\{1,2,\dots,2n\}$, show that there must be two such that one divides the other. This problem can be solved using mathematical induction, but feel free to solve it by other methods.
• Solve this self-referential test.