Sterling Stuart Stein (S³), working for Dr.Zeilberger in the REU program at Rutgers.
Here is the final presentation I gave (3 formats: HTML (view online), PPT, OO.o)

Alphametics Generator Letters stand for digits in an arithmetic problem. Given the answer, solve for which digit each letter stands for.
Example:  Solution:
  SEND       9567
+ MORE     + 1085
------     ------
 MONEY      10652
The program to generate the alphametics is finished. You can try it now using the web form. Alphametics-standalone
Hangman Have the computer play the game hangman. They should try to minimize the number of turns or number of wrong letters. The game is written and supports up to 9 players. Many computer strategies have been implemented. The computer can win in 5.1 guesses on average with 1.8 wrong. All of the statistics for the different strategies have been collected. Hangman
van der Waerden's Theorem Given a bit string long enough, there will always be a subsequence of k 0's or k 1's with their positions a fixed distance from each other.
Example: k=4
 ^ ^ ^ ^       ^^^^ 0: (1,2), (15,1)
   ^    ^    ^    ^    (3,5)
^   ^   ^   ^   ^      (0,4), (4,4)
  ^   ^   ^   ^     1: (2,4)
Implemented a O(n²) time algorithm for finding the longest chain in a bit string. It also works for a k-sized chain in O(n²/k) time. Brute force search for strings that don't contain a k-chain. van der Waerden