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 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 numbers from , 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.
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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.
numbers from
, 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.
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