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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.

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

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ 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
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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?

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  • $\begingroup$ 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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