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Russian Roulette (Posted on 2010-06-08) Difficulty: 4 of 5
Eight men, including Colonel Mustard, sit at a round table, for a modified game of Russian roulette. They are using a six chamber revolver which has been loaded with 5 bullets.

The game begins by one of the men reaching into a hat, and randomly drawing the name of the first player.

If the first player survives his turn, the gun is handed to his adjacent clockwise neighbor, and his name is immediately returned to the hat.

If the first player loses, his name is thrown away, and the men pull from the hat, and choose the name of the next player.

The game is continued in such a way until either all five bullets have fired, OR a player survives his turn, but no longer has an adjacent clockwise neighbor to pass the gun to.

What is the probability that the Colonel will survive the game?

(Note that the chamber is spun every time a player takes his turn).

No Solution Yet Submitted by John zadeh    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Implications? | Comment 7 of 12 |

I accept Charlie's argument, since it presumably gives the probability before the drawing for the first round (which is the only decisive way to interpret the challenge question).  At that stage, the same 61% probability would apply to each of the eight men.  As soon as the first name is drawn, the probabilties change radically: the first man has only 1/6 chance to survive (actually a bit worse odds, since if he survives the first round he could still be caught in a later round). 

This is a surprising result (if the proposer confirms the interpretation), and hence a good puzzle, even if an insipid "game".


  Posted by ed bottemiller on 2010-06-09 10:57:03
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