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?

only 1 drawing is enough i believe, that is if one takes out a ball from the box which is labelled BW only. as the three boxes are all incorrectly labelled, the ball took out would show everything: if it's white then this box contains 2 whites as it can't be BW, thus the WW box must contain 2 blacks and the BB box different colours. if it's black then it contains 2 blacks, the BB contains 2 whites and the WW different coulours. right?

Posted by fad on 2003-02-28 01:48:08