A puzzle by Ezra Brown and James Tanton:
Three gnomes sit in a circle. An evil villain places a hat on every gnome’s head. Every hat is both rouge or puce, the colour chosen by the toss of a coin. Every gnome can see the colour of his companions’ hats however not of his personal.
On the villain’s sign, all three gnomes should communicate directly, every both guessing the colour of his personal hat or saying “Go.” If at the very least considered one of them guesses appropriately and none guesses incorrectly, all three gnomes will stay. But when any of them guesses incorrectly, or if all three cross, they’ll all die.
They could not talk in any manner through the recreation, however they’ll confer beforehand. How can they prepare a 75 p.c probability that they’ll survive?
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Every gnome will cross until he sees that each of his companions are sporting hats of the identical coloration. In that case he’ll guess the alternative coloration. This produces a win in six of the eight attainable preparations of hats.
(Ezra Brown and James Tanton, “A Dozen Hat Problems,” Math Horizons 16:4 [April 2009], 22-25.)