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



closed as too broad by 6005, John, user127.0.0.1, Paul, user61527 Feb 5 '14 at 4:56

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  • $\begingroup$ I think a good big-list question should specify exactly what kind of problem it is looking for, not just a general statement like "creative easy combinatorics problems." $\endgroup$ – 6005 Feb 5 '14 at 4:17
  • $\begingroup$ I wan't that type of problems, asking how many marbles you need to take out to guarrantee. easy combinatorial maximization problems are also welcome. $\endgroup$ – Jorge Fernández Hidalgo Feb 5 '14 at 4:47

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?

  • $\begingroup$ My first guess would be "don't draw any marbles." :) $\endgroup$ – John Feb 5 '14 at 4:16
  • $\begingroup$ Alternately, "draw all the marbles" also gets you a score of 0. And that way you get to draw marbles =) $\endgroup$ – GMB Feb 5 '14 at 4:20
  • $\begingroup$ Draw until you're ahead and then quit. $\endgroup$ – qwr Feb 5 '14 at 4:36
  • $\begingroup$ Sounds like something related to sultan drowry. $\endgroup$ – Jorge Fernández Hidalgo Feb 5 '14 at 4:47
  • $\begingroup$ "Draw until you're ahead" isn't right, if I remember correctly. If your first draw is white, you should keep going, because there's a pretty good chance you'll hit +2 at some point in the future (even if your next draw drops you back to 0). $\endgroup$ – GMB Feb 5 '14 at 5:40

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