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?

Erm.. 1.

Take a ball from the box marked BW. Because all of the labels are incorrectly placed, whatever colour comes out the box will have two of that colour (either BB or WW).

The box marked BB or WW (whichever colour you picked out) will have to be the other option out of BB and WW, otherwise one will have the correct label.

These are the possible situations.

Take a ball from box marked BW. It is:
1. White. Therefore the box marked WW is actually BB and the box marked BB is actually BW.
Or
2.Black. Then, the box marked BB is actually WW and the box marked WW is actually BW.

Posted by Lewis on 2003-06-21 08:23:18