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?

Round 1 

Woman 1

See: (2) (2)

Thinks: I have either (2) or (3)

Answers: I don't Know

Woman 2

Sees: (2) (2)

Thinks: A.  I have either (2) or (3)

B. Woman 1 saw either (2) (2) or (2) (3)

C: woman 1 either thinks she has (2) or (3) OR (1) or (2)

D: I do not have a (1)

Answers: I don't Know

Woman 3

Sees: (2) (2)

Thinks: A.  I have either (2) or (3)

B. Woman 1 & Woman 2 saw either (2) (2) or (2) (3)

C: woman 1 & Woman 2 both think they have (2) or (3)

D: I do not have a (1)

E:If niether woman knows what they have got then niether woman saw a (3) therefore I have a (2)

Answers: I Have a (2)

ROUND 2

Woman 1 now now that niether of the other women saw a (3) and knows she has a (2)

Answers: I have a (2)

Woman 2 never gets to answer since the other 2 already have

 

Edited on December 16, 2005, 10:50 am

Posted by Wallace North on 2005-12-15 17:30:51