Common knowledge puzzles are my favorite. Here’s one I just came across. I challenge you to try to figure it out in less than 5 minutes. 🙂
Three perfect logicians with positive (non-zero) integers taped to their foreheads, A, B, and C, sit in a triangle. Each doesn’t know their own number but can see the numbers for the other two. It is common knowledge amongst all three that one of the numbers is the sum of the other two, but it is not known which is which.
A looks at B and C, and says “I don’t know what my number is.”
B thinks a moment and then says “Me neither.”
C thinks a moment and then says “Me neither.”
A thinks, then says “Now I know! My number is 25.”
What are the numbers on B and C’s foreheads?