Question 134446: There are three bins of marbles. They are labeled white, black, and mixed. Each bin is incorrectly labeled. You cannot see inside the bins. How can you draw one marble from one bin and then correctly label all the bins?
Found 2 solutions by vleith, Edwin McCravy:
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! Given that all three bins are mislabeled.
1)Pull a marble from the bin labeled mixed. Since the bin is mislabeled, this cannot be the mixed bin. Whatever color you draw must come from a bin with only that color in it. Set the mixed label on the ground
2) Whichever color you drew in step one (white or black), take the matching label from the bin that has that label on it and put it on the bin from step 1.
3) The bin that still has a label that you haven't touched is still mislabeled.
4) Move the label from step 3 bin to the other bin that doesn't yet have a label.
5) Move the mixed label to the only bin left without a label.
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
Draw one from the bin labeled "mixed". Re-label it with that same color.
Relabel the bin originally labeled with that color with the opposite color,
and re-label the remaining bin "mixed".
Explanation:
You know that the bin labeled "mixed" contains only marbles of the
same color, since it's incorrectly labeled.
So draw one marble from the bin labeled "mixed". If it is white then
it contains only white marbles, so re-label it correctly as "white".
Then the bin originally labeled "black" cannot contain only black
marbles since it is labeled incorrectly. And it certainly can't
contain only white marbles because you have just finished correctly
re-labeling the all-white bin! So it can only be the bin with mixed
colored marbles.
So the remaining bin, which was originally labeled "black" contains
only white marbles.
It's exactly the same explanation if you drew a black marble, except
you interchange the words "white" and "black".
Edwin
|
|
|
