Problem number 30. Adira keeps golden, red, black, pink, and white pearls in five small boxes. Each box contains pearls of only one color. The boxes are labeled as shown, and all the labels are true. Adira's friend Lily wants to know which box contains the golden pearls. She may open exactly one of the five boxes to look inside. Which box must Lily open to be certain which of the boxes contains the golden pearls? Intuitively, the box that will give us the most information is the box that's the least restricted. If we look at all the boxes, box D is the least restricted, because it only has not black, whereas all the other ones have two different colors, but D could theoretically have up to four different colors inside. That means that if we open it, it will probably give us the most information as to what box contains the golden pearls. Let's try opening box D and see what happens. If box D has the golden pearls, well then we're done. There's nothing else we have to do. Let's say we open box D and it has the red pearls. Well then box A says it has golden or red. So if D has the red pearls, then A must have the golden pearls. Similarly, if box D happens to have the pink pearls inside, then looking at box B, we know that it must have the black pearls. And now, if we look at C, C says black or golden, but we already know B must have the black pearls. So in this case, C must be the one with the golden pearls. Now let's say we open box D and it has the white pearls. Then E, since it says pink or white, since we already know D has the white pearls, then box E must have the pink pearls. This means that like before, box B must have the black pearls, since we already know where the pink pearls are. And finally, just like before, box C, since we already know where the black pearls are, must have the golden pearls. This means that in all cases, we'll know from opening box D, which box has the golden pearls. So the answer is D.

golden pearls

box D

process of elimination

informative choice

pearl colors