Today on X, I came across a supposed Goldman Sachs interview question labeled “Logical Deduction Question”. Here’s how it goes:
“There are three boxes on a table. One contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes are labeled incorrectly. You can pick one fruit from one box, but after that, you must correctly label all boxes. How do you do this?”
By all means, take a moment to try to solve it. This is a perfect example of a poorly formulated question–so poorly, in fact, as to lose any right answer it might have had. As such, it makes a good example from which to learn good philosophy (or at least philosophy at a level the question writer and approvers apparently failed to attain).
There are two substantial problems with the question. One is semantic ambiguity, and the other is a missing assumption. First, regarding the ambiguity, consider the statement L above, “The boxes are labeled incorrectly.” This is ambiguous between (a) “Each box is mislabeled” and (b) “The boxes as a whole are mislabeled.” For a to be true, all three boxes must have a false label; for b to be true, only one box need have a false label (and others may or may not have false labels as well). Unfortunately, no matter which of these meanings you choose, the question is still unanswerable as stated because of the other problem of a missing assumption.
Second, regarding the missing assumption, the question becomes answerable if you assign meaning a to L and add the assumption that the boxes are labeled “Apples”, “Oranges”, and “Mixed” (or “Apples and Oranges” or similar). To solve, you take one fruit from the box labeled “Mixed”. You know the box is not mixed because each box is mislabeled. Remove the “Mixed” label and move the “Apples” or “Oranges” label to the box you tested based on what fruit you removed. Set the tested box aside. Move the label from the remaining labeled box to the unabled one. Put the “Mixed” label on the last unlabeled box. Problem solved. The problem with this solution, of course, is that it requires a new assumption. Neither L (whether interpreted as a or b) nor anything else in the question entails this assumption: the three labels could be “Apples”, “Oranges”, and “Watermelons”, for example.
Even if you add the missing assumption to the question, it is still unanswerable as stated because of the ambiguity in L. So the question is doubly unanswerable. The solution I’ve given is the only one, to my knowledge.
I would be remiss if I didn’t also mention the virtue of concision. The reason why it is considered a mark of genius is that it tends to get traded for other virtues like clarity and informativeness. As you try to make an utterance more concise, you will eventually have to start sacrificing clarity and important information. What clarity and information you can afford to lose is part of the balancing act. Lean too heavily toward those and your speech will become pedantic. Speaking very concisely while also being clear and informative can be a real artform. In the example above, concision could have been a reason the question became poorly formed and lost both clarity and important information. How might we reform the question to achieve a good balance? Here’s my attempt:
“There are three boxes labeled ‘Apples’, ‘Oranges’, and ‘Mixed’. One box has only apples, one has only oranges, and one has both apples and oranges. The boxes are all mislabeled. You can pick one fruit from one box, but after that, you must correctly label all boxes. How do you do this?”
Hopefully you learned something from this. I would be annoyed to find this is a real interview question from Goldman Sachs: one of my pet peeves is when someone tries to get clever but is too incompetent to do so.
