### 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 :)

2. 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

3. 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