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?

Woman A would know what his number was if he saw a 1. So Woman B and Woman C can't have a 1, but A doesn't know if she has a 2 or a 3

Woman B would know what her number was if she saw a 1. Also, if she saw a 3, she would know her number was 2 (since it isn't 1) So Woman A and Woman C can't have a 1 or a 3, but B doesn't know if she has a 2 or a 3.

Woman C knows she has a 2.

Woman A knows she has a 2.

Woman B interestingly enough still doesn't know what her number is, because B knew what A and C's numbers were before they knew, and thus they don't reveal any more information when they say they know.

Posted by Gamer on 2005-12-15 12:59:16