WUSTL ESE 523 - ProblemSet1-2013 (3 pages)

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ProblemSet1-2013



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ProblemSet1-2013

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Pages:
3
School:
Washington University in St. Louis
Course:
Ese 523 - Information Theory
Information Theory Documents

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ESE 523 Introduction to Information Theory Professor Joseph A O Sullivan Fall 2013 Problem Set 1 Due Tuesday September 16 2013 Suggested Problems 1 Look over the problems at the end of chapter 2 2 Problem 2 9 Required Problems 1 Problem 2 1 2 Problem 2 6 3 Problem 2 10 4 Problem 2 12 5 Problem 2 16 6 Solve the problem from the New York Times article see below for three players and for seven players April 10 2001 Why Mathematicians Now Care About Their Hat Color By SARA ROBINSON ERKELEY Calif April 9 It takes a particularly clever puzzle to stump a mind accustomed to performing mental gymnastics So it s no ordinary puzzle that s spreading through networks of mathematicians like a juicy bit of gossip Known as the hat problem in its most popular incarnation this seemingly simple puzzle is consuming brain cycles at universities and research labs across the country and has become a vibrant topic of discussion on the Internet The reason this problem is so captivating mathematicians say is that it is not just a recreational puzzle to be solved and put away Rather it has deep and unexpected connections to coding theory an active area of mathematical research with broad applications in telecommunications and computer science In their attempts to devise a complete solution to the problem researchers are proving new theorems in coding theory that may have applications well beyond mathematical puzzles This puzzle is unique since it connects to unsolved mathematical questions said Dr Joe Buhler deputy director of the Mathematical Sciences Research Institute here and a hat problem enthusiast The hat problem goes like this Three players enter a room and a red or blue hat is placed on each person s head The color of each hat is determined by a coin toss with the outcome of one coin toss having no effect on the others Each person can see the other players hats but not his own No communication of any sort is allowed except for an initial strategy session before the game begins Once



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