A problem by Kevin Yang
The first box has two white balls. The second box has two black balls. The third box has a white and a black ball.
Boxes are labeled for their contents but all labels are wrong!
You are allowed to open one box, pick one ball at random, see its color and put it back into the box, without seeing the color of the other ball.
How many such operations are necessary to correctly label the boxes?
The answer is 1.
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1 solution
If you pick a white ball from a box, there are only 2 possibilities: either that box has 1 white and 1 black or both are white. Similarly, if you pick a black ball from a box, there are also 2 possibilities: either that box contains 1 white and 1 black or both are black. Either way, since we are told that all labels are wrong, the correct label on this box has to be the other possibility mentioned (hope you guys know what I mean).
Having determined the label for one box, we are down to only 2 boxes. Since we are told that all labels are wrong, we need not perform another similar operation. Simply swap the labels!! :)