There are three boxes on a table, each with a label. Thomas knows that one box contains grapes, one box contains cherries, and the third box contains both grapes and cherries. He also knows that the three labels used—grapes, cherries, and grapes and cherries—were mixed up and that none of the boxes received the correct label. He opens just one box and, without looking into the box, takes out one piece of fruit. He looks at the fruit and immediately labels all the boxes correctly. Which box did Thomas open? How did he know how to correctly label the boxes?