Three women were seated around a table. After blindfolded, a numbered disc was pasted on each of their foreheads. The women were truthfully told "Each of you has either a 1, a 2 or a 3 on your forehead, and the sum of your numbers is either 6 or 7".
After the blindfolds were removed, each woman in turn was asked to name the number on her forehead without seeing it. The question was repeated until only one woman failed to name the number on her forehead.
When it was logically possible to name the number on her forehead, each woman did so; when it was not logically possible to name the number on her forehead, she would said "I donīt know my number", and waited until the question was repeated to her next time around.
Each woman had a 2 on her forehead. Which woman failed to name her number?
The last thing you can say is that C on Round 2, after A and B say they are a 2, still doesn't know if she is a 2 or a 3.
She could of course be a 2, following the logic of the last commet.
And if she were a 3, the sequence would have been the same:
A would have seen a 2 and a 3 and said, "I'm a 1 or a 2," => so "I don't know my number."
B would have also seen a 2 and a 3 and said the same.
C sees a 2 and a 2 and still doesn't know if she's a 2 or a 3.
Round 2:
A knows that C doesn't know, so A can't be a 1 and says, "I'm a 2."
B says the same thing: "If I were a 1, C would have known that she was a 3 on the first round, so I can't be a 1, so I'm a 2."
So C on the 2nd round still can't say if she's a 2 or a 3. She still has to say, "I don't know my number."
And that's my final answer ...
Maybe this is it (cont.)
