The Salem Witches Puzzle

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Here's a puzzle I heard in a different form some considerable time ago, but reworked into this form by James Grime.

Clever James.
Two friends are accused of witchcraft by the Witch Finder General (WFG), their future looks grim, and they are rather depressed. They perk up somewhat, though, when the WFG announces his test. They are to be separated, and each has to flip a coin. Then each has to predict the result of the other coin flip.

The WFG claims that if they're both right then they're obviously in league with the devil, and will be declared guilty and burned as witches.

Our friends are worried, but not too depressed. Clearly each has a 50% chance of getting it right just by guessing, so they only have a 25% chance of both being right, so they have a 75% chance of getting off.

Then comes the hammer blow: the test will be run 50 times.

Bother. That gives a less than 1 in a million chance.

Our friends are clever though, and they devise a strategy that guarantees their survival.



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