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?

One draw is needed. Take one ball out of the box marked BW and you will get either a black or white ball. If you get a Black, then it has to contain two black balls because it can't contain one black and one white. Since the box marked WW can't have both white and we know where both black is, we know white has one of each color. Since the last box remaining is BB, and the last balls remaining is the white-white combination, they have to go together. When you pull a ball out of the BW box that is white, the same reasoning applies except switch everyy black from the previous explanation to white, andd all white to black.

Posted by Jon on 2003-04-11 05:57:33