MATC Mathematics Club
Madison Area Technical College
Professor Benedek Valko
"Random permutations and suitcases"
Previous presentation: "Dominos and Determinants"
Abstract: Suppose that in a game show there are 20 briefcases each containing an unknown amount of money. The contestant can open the briefcases one-by-one and at any point she can decide to take the money from the just opened briefcase (that's her prize) or continue opening them. She cannot go back to a previous, opened briefcase and if she opens all of them, then she gets the money from the last briefcase. If we knew the values of the briefcases at the beginning of the game then it would be easy to get the grand prize (the largest possible sum): we could just open the briefcases until we get to it. But what if we don't know the sums at the beginning? How should we play if want to have the highest chance of winning the grand prize? How big is that chance? And what happens if we have 100 or 1.000.000 suitcases?
Benedek Valko received his PhD from the Technical University of Budapest (Hungary) and has been a member of the Department of Mathematics from 2008. His main interest is probability theory. He is the director of the Wisconsin Mathematics, Engineering and Science Talent Search
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