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).
It was not the puzzle which I considered insipid (it is really quite a challenge), but the mise-en-scene. Charlie seems not to consider the odds that all survive (perhaps the firing mechanism is defective, or the spin is biased to select only the one empty cylinder): of course in that case the game would not come to an end under its announced condition. We are not told at what pace they take turns -- perhaps they meet only once a decade, and take up where they left off. Perhaps one dies of natural causes, but was placed to the left of the next to be drawn, thus ending the game. If we could get the solution to come out to something like the cube root of e / pi -- then we could explore that. But, seriously folks...
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