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

Knows: Total is 6 or 7

Sees: 2 and 2

Thinks: I must have a 2 or a 3

Answers: I Don't Know

WOMAN B

Knows: C has a 2

Thinks: A can see 1-2; 2-2 or 3-2

Hears: I Don't Know from A

Thinks: If I had a 1, A would know she has a 3 so I must have a 2 or a 3

Answers: I Don't Know

WOMAN C

Hears: I Don't Know from A

Thinks: As for B – I must have a 2 or 3

Hears: I Don't Know from B

Thinks: B knows A has a 2, and she has a 2 or 3. If I had a 3 B would know she has a 2 so I must have a 2

Answers: I Have a 2

WOMAN A:

Thinks: If I had a 1 B would have known she had a 3; If I had a 3 B could reason she must have a 2 since if she had a 1 I would have known my number was 3.

Answers: I have a 2

B failed to realise her number

Thanks Paulo

Edited on December 15, 2005, 2:18 pm

Posted by Vernon Lewis on 2005-12-15 14:14:49