Puzzle #43: The Triangle Duel

Yet another wonderful puzzle from the Martin Gardner collection. This one is from “More Mathematical Puzzles and Diversions”, Chapter 5, Puzzle #9. This one involves probability, and hence difficult for children who do not understand probability at all.

Three men, Smith, Brown, and Jones, agree to participate in a pistol “duel.” The three men decide who goes first by drawing straws and each man is to wait their turn before firing upon either of the other men. After the first round of shots fired, the men will proceed in the same order until there is one man standing. All three men know that Smith is 100% accurate, Brown is 80% accurate, and Jones is 50% accurate.

Assuming that all three men are intelligent, logical thinkers, who has the best chance of winning? What is each man’s probability of surviving?

Note: the second question is a bit more difficult, so not for children.

As always, please send your answers directly to me at alokgoyal_2001@yahoo.com. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.

Happy dueling!


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