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?

Smallest number of drawings required to do this is ONE.

EXPLANATION

We draw precisely 1 ball from the incorrectly labelled BW jar.

Since it is incorrectly labelled, the BW jar either contains two black balls or two white balls. ............(i)

CASE-1: The ball drawn from BW jar is white.

Then, by (i), the other ball must be white. So, this jar is relabelled as WW.

Therefore, BB jar cannot contain two white balls. Also, being incorrectly labelled it cannot contain 2 black balls. Threfore, it must contain precisely 1 black and 1 white ball. So, this jar is relabelled as BW.

The remaining jar, that is WW must then be relabelled as BB.

CASE-2: THE ball drawn from BW jar is black.

Then, following arguments similar to Case-1, the BW jar should be relabelled as BB.

The WW jar should be relabelled as BW, and:

BW jar should be relabelled as WW.