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 :)
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Source: Sent to me by Gaurav Sinha Problem: Siddhant writes a Maths test and correctly answers 5 out of 6 Arithmetic questions and 20...
Is the answer 0?
ReplyDeletenope :(
ReplyDeleteSince no one has been able to solve it till now, probably this would help.
ReplyDeleteThe 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
Isn't it just e^1 ??
ReplyDeleteBecause prob. of not being shot by a person when theyre are n people alive is 11/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 (11/n)^n after n round.
So I get e^1