## Friday, October 09, 2009

### Marbles in Boxes

There are three boxes in front of you.  They are labeled BB, WW and BW.  In one box, there are two black marbles, in another there are two white marbles.  In the third box there is one black and one white marble.

No label corresponds to the marbles in its box.

What would be the smallest number of marbles that must be randomly picked, from one or several boxes, to identify their contents?

1. I think you only have to draw one marble from the box marked BW.

Since none of the starting labels can be correct...

If the marble you draw is white, you know that the BW box contains white-white. The BB box can't be black-black, so it must be black-white. Then the WW box must be black-black.

Likewise, if you draw a black marble from the BW box, then BW=black-black, WW=black-white, BB=white-white.

2. Wow, nicely done, Andy.

3. Wow, great job explaining it, Andy! I think that's what I got.....

4. It's amazing how this one works out. My first thoughts when I read this one (You didn't think I made it up, did you?) was along the lines of three or more. It's that key line: 'no label corresponds to the marbles in its box' that makes the difference.

Well done Andy, especially with the explanation. One marble is the correct answer.

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