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?

Thanks pcb - nice problem

1. First box contained 2 Blacks so started BBB or BBW.

2. Since first girl can identify third ball, label (incorrect) must also be BBB or BBW to eliminate one possibility.

3. Similarly second box with 1 Black and 1 White contains BWW or BBW and is labelled BWW or BBW.

4. Third box has 2 Whites so contains BWW or WWW.

5. Since third girl CANNOT identify the third ball her box cannot be labelled BWW or WWW.

6. So must be labelled BBB or BBW.

Summary.

Box 1 started BBB or BBW. Label BBB or BBW

Box 2 started BWW or BBW. Label BWW or BBW

Box 3 started BWW or WWW. Label BBB or BBW

7. From 1 and 6 First and third boxes are labelled BBB and BBW so second box cannot be labelled BBW and must be labelled BWW.

8. Second box label (BWW) is incorrect so from 3 started BBW.

9. From 1. and 8. first box must have started BBB and incorrectly labelled BBW

10 From 6. and 7. Box 3 Label BBB

11. By elimination Box 4 Labelled WWW.

12. From 11 Box 4 cannot have started WWW (Label must be incorrect) so Box 3

14. By elimination Box 4 started BWW.

Summary.

Box 1 started BBB. Label BBW. Removed 2 Black. White remains in box

Box 2 started BBW. Label BWW Removed 1 Black and 1 White. Black remains in box

Box 3 started WWW. Label BBB. Removed 2 White. White remains in box

Box 4 started BWW. Label WWW

Posted by Vernon Lewis on 2008-06-19 19:08:22