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 first woman to whom the question posed is the one who will be failed to answer.

Explanation:

The first woman after faced the question will see the heads of other 2 ladies and founds 2's on their heads. so she can conclude that the number on her head could be either 2 or 3 because the sum can either be 6 or 7. so she says "I don't know".

when the question goes to 2 lady, she also see the same thing that the other 2 ladies have 2's on their heads. so she also can have a 2 or 3 on her head. but from the conclusion of 1 lady she can easily found her number on her head is 2 because if it is 3 the 1 lady could easily have told her number as 2.

when the question goes to 3 lady, she also see the same thing that the other 2 ladies have 2's on their heads. so she also can have a 2 or 3 on her head. but from the conclusion of 1 lady she can easily found her number on her head is 2 because if it is 3 the 1 lady could easily have told her number as 2.

but even after these conclusions, the 1 lady can never know that the number on her face is 2.

 

Posted by surya on 2005-12-21 05:07:30