Imagine that you have three boxes, one containing two black balls, one containing two white balls, and the third containing one black ball and one white ball.
The boxes were originally labelled for their contents (BB - WW - BW) but someone has inadvertently switched the labels so that now every box is incorrectly labelled.
Without looking inside, you are allowed to take one ball at a time out of any box that you wish, and by this process of sampling, you are to determine the contents of all three boxes.
What is the smallest number of drawings needed to do this?
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Solution: see comment
Thursday 11 October 2007
Logic Puzzle: Black & White Balls
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22 comments:
You only need to take one ball to re-label the jars properly. The key is that all the labels are wrong. So, the jar labeled BW has either all black balls or all white balls. Take one ball from that jar, and figure out which one it is.
Now, if this is the black jar, then the jar labeled "black" is really the white jar, and the remaining one is mixed.
That doesn't seem like the correct answer. It assumes that the premises you gave in the beginning were wrong, in which case anything could happen.
Isn't the minimum number 3?
The question asks the minimum number of draws needed to find out the answer, so we can assume ideal conditions occur. There are three boxes, one with each of the three combinations. So, if you happen to pick up the real BW box first, then you look at the first ball, put it back in, take out the other one, and you know you have the BW box. Then, you only need to take out one ball from either of the other two boxes and you will know which box contains which balls.
no, because all labels are wrong, each box only has 2 possible combination. by choosing mixed box first, you'll know the answer straight away.
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