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The Department of Mathematics Challenge of the Week

A solution and a new problem is posted every Monday during fall and spring semesters at www.cs.colostate.edu/~rmm

Email your solutions to solution@math.colostate.edu

One winner each week is eligible for a free ice cream and topping, courtesy of Cold Stone Creamery.

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Challenge 1, Fall '04

After spending an evening at a saloon, three cowboys get into an argument and decide to settle it with a "three-way duel." Cowboy 1 will take a shot, possibly killing one of the other two. Cowboy 2, if he is still alive, will then take a shot. Cowboy 3 will then take a shot if he is still alive, after which it will be Cowboy 1's turn again, if he is still alive. The turn goes round and round the circle until only one cowboy is standing.

Cowboy 3 is a good shot and can hit his target every time. Cowboy 2 can only hit his target with a probability of 2/3. Cowboy 1 drank a lot of whiskey, and can only hit his target with a probability of 1/3. All three cowboys know these things about each other.

You are Cowboy 1 and the duel is starting. What can you do to maximize your chances of survival?

Hint: There is a way to ensure that your chance of survival is strictly greater than 1/3.

Click Here for the Solution