# More Balls and Boxes

THUDandBLUNDER
Posers and Puzzles 06 Nov '04 08:48
1. 06 Nov '04 08:48
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 white balls.
One box contained 3 white balls.

Each box had a label on it reading &quot;BBB&quot; (Three Black) or &quot;BBW&quot; (Two Black, One White) or &quot;BWW&quot; (One Black, Two White) or &quot;WWW&quot; (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, their colors were announced for all the girls to hear but the girls cold not see the labels on any other box other than their own.

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

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

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

Finally, the fourth girl declared: &quot;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.&quot;

The first three girls were amazed by the 4thh girl's assertion and promptly challenged her. She proceeded to identify everything that she said she could.

Can you do the same?
2. 06 Nov '04 10:04
I can.

The first girl draws BB and sees on her label either BBB or BBW so given that the label is wrong, knows the third ball.
The second girl draws BW and has the label BBW or BWW.
The third girl draws WW and has the label BBB or BBW (otherwise she would know the third ball).
So the second girl has the label BWW, because either 1 or 3 has label BBW. Therefore, the second girl has balls BBW, and 1 has balls BBB
The fourth girl knows that she has the label WWW and that 3 has balls WWW and label BBB. So 4 has balls BWW

So:

g label balls
1 BBW BBB
2 BWW BBW
3 BBB WWW
4 WWW BWW
3. 06 Nov '04 10:57
Originally posted by piderman
I can.

Well done. In fact, the 3rd girl could have, but she ain't too bright.
Well done, piderman. In fact, the 3rd girl could have, but she ain't too bright.
4. Nemesio
Ursulakantor
07 Nov '04 00:291 edit
Originally posted by THUDandBLUNDER
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 first girl, having drawn two black balls, looked at her label and announced: &quot;I know the color of the third ball!&quot;

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: &quot;I too know the color of the third ball!&quot;

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: &quot;I can't tell the color of the third ball.&quot;

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: &quot;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.&quot;

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.

Nemesio
5. 07 Nov '04 18:45
Originally posted by nemesio
The first girl, having drawn two black balls, looked at her label and announced: "I know the color of the third ball!"

The box must have been labeled BBW and thus, she knew the other ball was black (she had BBB).
That conclusion is too quick. The other way around is also possible. Had the box been labeled BBB, she would have BBW.
6. 08 Nov '04 11:56
containing different colored balls - right....

so they're all wrong, b/c there can't be a box with www or bbb ðŸ˜‰
7. 08 Nov '04 16:24
Originally posted by ShadowGnu
containing different colored balls - right....

so they're all wrong, b/c there can't be a box with www or bbb ðŸ˜‰
nah, the balls are different, not the colours ðŸ˜›ðŸ˜€