Here’s a simplified version of a similar colored stamps puzzle (it was once a question thrown at me during an interview). The approach can be the same to the one indicated by Felix in the previous post, but if you haven’t seen it, it might still be interesting:
In a game show, the host placed one colored stamp on each of the three contestants’ forehead. It could either be a red or a blue stamp. Each contestant can only see the other guys’ stamps, but not his own. The host gives an important clue: at least one of the stamps is red. The host then asks each contestant to shout the color of the stamp on the contestant’s forehead. Here are the responses, in order:
A: “I don’t know”
B: “I don’t know”
C: “I know!”
What is the color of C’s stamp and what is his thought process leading to a confident answer?
Posted by suhendry on November 8, 2010 at 11:24 am
Assuming A, B and C are good logicians, B knew A’s answer and C knew A’s and B’s answer before his turn.
If A saw two blues then he could easily conclude that his was red since the host said there is at least one red stamp, but he didn’t. It means A saw one red and one blue, or two reds.
If B saw C had a blue stamp, then he could conclude that his stamp was red since there must be at least red on B or C (based on why A couldn’t answer). But again, B didn’t know, it means he saw a red stamp on C’s forehead so he didn’t know whether he has a blue or a red one.
Based on A’s and B’s answer, C could conclude that he had a RED stamp on his forehead.
Posted by turuthok on November 8, 2010 at 5:37 pm
Correct!