Originally posted by THUDandBLUNDER
The first girl, having drawn two black balls, looked at her label and announced: "I know the color of the third ball!"
Four girls were blindfolded and were each 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 wh ...[text shortened]... tify everything that she said she could.
Can you do the same?
The box must have been labeled BBW and thus, she knew the other ball was black (she had BBB).
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 box must have been labeled WWB and, thus she knew the other ball must be black. (She had BBW).
The third girl withdrew two white balls, looked at her label, and said: "I can't tell the color of the third ball."
The box must have been labeled BBB, so she didn't have enough information to discern whether she had WWW or WWB (not knowing the other labels).
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."
Since one can deduce that she had the box labeled WWW, and given that she can't have WWW, she must have WWB. (which means girl 3 has WWB).
Girl #1: Balls BBB; Box BBW;
Girl #2: Balls BBW; Box WWB;
Girl #3: Balls WWW; Box BBB;
Girl #4: Balls WWB; Box WWW.