Three boxes each contain a number of billiard balls. One box contains only even-numbered balls, one box contains only odd numbered billiard balls, and the third box contains a mixture of odd and even numbered balls. All the boxes are mislabeled. By selecting one ball from only one of the boxes, can you correctly label the three boxes?

Question

Explain why or why not.

Answer 1

Let the boxes be E,O,M.
Draw a ball from E. If it is even, then the box marked O must contain the even balls, because otherwise the M box would contain the evens, leaving O containing the odds. But O is mislabeled, so it must contain the evens.

So, drawing an even ball from the E box means that

E should be M
O should be E
M should be O