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.
Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: