Today’s puzzle is a new twist on a classic genre: the “common knowledge” hat riddle in which logicians deduce facts about their hats based on what they know, and what they know others know.
Head sums
Ade, Binky, and Carl are honest perfect logicians. A hat is placed on each of their heads. Each hat has a whole number larger than zero written on it, which the other two logicians can see but which the wearer cannot. One of these numbers is the sum of the other two (so for example, the three numbers could be 3, 7, 4, or another possibility is 6, 6, 12). All of this is public knowledge.
Ade sees that Binky has a 3 and Carl has a 1.
Ade says for all to hear: “ I do not know the number on my hat”
Binky then announces: “I do not know the number on my hat”
Ade then announces: “I know the number on my hat!”
What number is on Ade’s hat?
I’ll be back at 5pm UK with the solution. PLEASE NO SPOILERS. Please discuss hats.
UPDATE: Read the solution here.
The puzzle was devised by Timothy Chow, inspired by a puzzle by Dick Hess.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
