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Who should you shoot first?

Posted on: October 28th, 2013 by

A, B and C are playing a shooting game. Each person takes a turn to shoot at one of the others until there's only one standing.
A has a probability 1/3 of hitting the mark.
B has a probability 2/3 of hitting the mark.
C is accurate and will definitely hit the mark.
The shooting order is A,B,C,A,B,C,.... indefinitely until only 1 person is left alive. If a person is dead, we skip his turn.
Who should A shoot first?

- A classic puzzle

4 Responses to Who should you shoot first?

  1. Dinesh had this to say about that:

    I don't see any incentive for A to try shooting B. If he does kill B, he will surely be killed by C in the next round. So, I guess A should always try to kill C and then take his chances with B.

    • admin had this to say about that:

      There is a better solution.

      • Rohit had this to say about that:

        The key is survival rate. When C gets his turn, he will try to get rid of the guy with the higher probability. Hence, B will try to shoot C. A will also try to shoot C as per the above comment by Dinesh because he has better chances of survival.

  2. Sid Hollander had this to say about that:

    I think that A should point at B and shoot to MISS! This serves to postpone his eventual duel with C who perchance MAY be killed by a lucky shot from B.

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