The Probabilistic Method Part 2

You have a bag of marbles. The probability of picking a blue marble out of the bag is 1/3. The easiest conclusion to make at this point is that there must be a blue marble in the bag.

We will apply this logic to a variety of problems from number theory, geometry and other fields to turn seemingly difficult questions into simple combinatorial ones. While a follow up to part 1 of this series covering a broader range of topics, this talk will be self-contained