This puzzle is cribbed from "Fermat's Last Theorem" by Simon Singh, which I recommend highly, by the way. (I mean the book.)
A 'truel' is a duel involving three people. The rules are that each has a turn at shooting at one opponent and the truel continues until only one participant is left alive.
In one particular truel there are three people: Mr Black, Mr Gray and Mr White. Mr Black hits his target one time in three, Mr Gray hits the target two times in every three shots and Mr White never misses. To make it fairer Mr Black shoots first, then Mr Gray, followed by Mr White, and so on, until only one man remains alive.
The question is what should Mr Black do?
No, the answer is not "take shooting lessons".
To receive bonus points, what are each man's chances of
surviving the ordeal?
Solution