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?
You would need to draw three balls. Let me explian.
First you would need to take one ball out of two of the boxes.
If you draw out two white balls then you know the box you didn't draw from is the all black box.
Then for your third draw you pull another ball out of one of the boxs you just pulled from if you draw out a black ball from that box then that is your mixed box.
The one left would then have to be the all white box.
up a tree
