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went to take the Putnam Math Contest today. here are 4 questions from it (not the most difficult ones). everybody is welcome to try them and share your excellent ideas. university freshman level math is more than enough.
Question 1:
An integer n, unknown to you, has been randomly chosen in the interval [1,2002] with uniform probability. your objective is to select n in an odd number of guesses. after each incorrect guess, you are informed whether n is higher or lower, and you must guess an integer on your next turn among the numbers that are still feasibly correct. show that you have a stratedy so that the chance of winning is greater than 2/3. |
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