I would like cool problems of the following style: how many marbles need to be taken out of a jar to guarantee we have one of each color? I need some cool problems for some classes I want to give to my math olympiad teammates. Thank you very much
Regards.
This is a little harder than your example, but ...
A jar contains 50 white marbles and 50 black marbles. You will play a game where you draw one marble at a time (uniformly at random, without replacement), and you can stop any time you like. Your score is (whites drawn - blacks drawn). What strategy should you play to maximize your expected score?