Can you solve it? Chapeau! A smart new hat puzzle | Mathematics
Today’s puzzle is a new take on a classic genre: the “common knowledge” hat riddle in which logicians infer facts about their hats based on what they know and what they know others know.
Main sums
Ade, Binky and Carl are honest and perfect logicians. A hat is placed on each of their heads. Each hat has an integer greater than zero on it, which the other two logicians can see but 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). This is all public knowledge.
Ade sees that Binky has a 3 and Carl has a 1.
Ade publicly says: ‘I don’t know the number on my hat’
Binky then announces: “I don’t 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 in the UK with the solution. PLEASE NO SPOILERS. Please discuss hats.
UPDATE: Read the solution here.
The puzzle was designed by Timothy Chow, inspired by a Dick Hess puzzle.
I’ve been putting up a puzzle here every other Monday since 2015. I’m always looking for great puzzles. If you want to suggest one, send me an email.
