Happy Thanksgiving everyone! Since my brother and I are on different coasts, this year’s festivities will be the first time that we won’t have the chance to talk about math puzzles around the Thanksgiving table. In honor of his absence, I present this fiendishly difficult “hats” puzzle:
Trogdor the Burninator is at it again, except this time he has hit the mother lode and captured an infinite number of peasants. As always, the peasants can escape their doom if they can figure out what color hat (either red or blue) Trogdor has placed on their heads. All the peasants guess simultaneously (no post-hat-placement communication), all peasants can see all the other hats on their peers’ heads, and the peasants can discuss strategy beforehand (though Trogdor will listen in). If only a finite number of peasants guess incorrectly, all the peasants go free; if not, Burnination for all. Can you help the peasants?
I can’t. I have a decent solution for a countably infinite number of peasants, but apparently there is a math-y way to save an uncountably infinite number of peasants too!
Good luck to all, and I hope this puzzle helps keep you entertained this weekend :)