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The girls, the boxes and the balls (Posted on 2008-06-19) Difficulty: 3 of 5
Four girls were blindfolded and each was given an identical box, containing different colored balls:

One box contained 3 black balls.
One box contained 2 black balls and 1 white ball.
One box contained 1 black ball and 2 white balls.
One box contained 3 white balls.

Each box had a label on it reading "BBB" (Three Black) or "BBW" (Two Black, One White) or "BWW" (One Black, Two White) or "WWW" (Three White). The girls were told that none of the four labels correctly described the contents of the box to which it was attached.

Each girl was told to draw two balls from her box, at which point the blindfold would be removed so that she could see the two balls in her hand and the label on the box assigned to her. She was given the task of trying to guess the color of the ball remaining in her box.

As each girl drew balls from her box, her colors were announced for all the girls to hear, but the girls could not see the labels on any boxes other than their own.

The first girl, having drawn two black balls, looked at her label and announced: "I know the color of the third ball!"

The second girl drew one white and one black ball, looked at her label and similarly stated: "I too know the color of the third ball!"

The third girl drew two white balls, looked at her label, and said: "I can't tell the color of the third ball."

Finally, the fourth girl declared: "I don't need to remove my blindfold or any balls from my box, and yet I know the color of all three of them. What's more, I know the color of the third ball in each of the other boxes, as well as the labels of each of the boxes that you have."

The first three girls were amazed by the fourth girl's assertion and promptly challenged her. She proceeded to identify everything that she said she could.

Can you do the same?

See The Solution Submitted by pcbouhid    
Rating: 4.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): The third girl didn't apply logic.... (Spoiler) | Comment 8 of 9 |
(In reply to re: The third girl didn't apply logic.... (Spoiler) by pcbouhid)

Assuming the 4th box's label is a typo and was meant as "BBW"....
The situation where the 1st girl's box is labelled "BBB" with her 3rd ball White and the 2nd girl's box labelled "BWW" with her 3rd ball Black would mean both girls had 2 Black balls and 1 White ball in their respective box. This situation is not possible by the given condition that each box contained a unique set of balls.

  Posted by Dej Mar on 2008-06-27 01:24:48
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