Some problem solving challenges that I tackled.

1- The 10 word guessing challenge:

Alice and Bob play the following game: Alice chooses a 10-letter word from a fixed dictionary, uniformly at random At each turn Bob proposes a word from the same dictionary For each proposal, Alice returns the "score" of the proposed word: each correct letter gives 1 point, plus an additional point if it is at the right position. The total score of Bob is the sum of scores over k rounds with k fixed to 5, 10 or 15. The goal is to maximize the score of Bob over 100 games - where each game lasts k rounds - (or its expectation). The score is then normalized so that the maximum score is 100.