Shoot me!!

Source: P. Winkler

In a room stand n armed and angry people. At each chime of a clock, everyone simultaneously spins around and shoots a random other person. The persons shot fall dead and the survivors spin and shoot again at the next chime. Eventually, either everyone is dead or there is a single survivor.

As n grows, what is the limiting probabality that there will be a survivor. :)

Treat at H8 canteen for the person solving it first :)

Comments

  1. Since no one has been able to solve it till now, probably this would help.

    The limiting probability does not exist in the sense that the probability does not approach a unique value

    Since source is Winkler, you are sure that its correct :P

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  2. Isn't it just e^-1 ??

    Because prob. of not being shot by a person when theyre are n people alive is 1-1/n

    Now prob. of at least one person alive we use inclusion exclsion principle, but when n is large this approx holds:

    Prob of not being shot is (1-1/n)^n after n round.

    So I get e^-1

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