Four philosophers - Plato, Socrates, Diogenes and Aristotle - had thirteen small cakes between them on a plate and they helped themselves as they went along, too busy to pay very close attention as to whether each man received his fair share. After a while, all the cakes were eaten, and the following discussion ensued:

Plato: Did you eat more cakes than I did, Socrates?

Socrates: I don’t know. Did you eat more cakes than I did, Diogenes?

Diogenes: I don’t know.

Aristotle: Aha!

Aristotle now knew how many cakes everyone had eaten - and, of course, knowing that Aristotle knew, the other three were able to make the same deduction. Given that:

- All four were extremely intelligent, flawlessly logical, and knew that their fellows were too
- Prior to the discussion, each of them knew only that everyone had eaten at least one cake
- Each knew how many cakes he himself had eaten
- None of them would dream of asking a question to which he already knew the answer

How many cakes did everyone eat?

[spoiler]Socrates knows that Plato ate at least one cake. His reply tells us that he himself ate at least two, or else he would have answered “No”.

Diogenes, knowing that Socrates ate at least two cakes, does not reply “No”, which would have meant that he himself ate only one or two, so he must have eaten at least three.

Plato now knows that the first three philosophers ate at least six cakes between them. The fact that he also knows exactly how many cakes everyone ate proves that he must have eaten seven, as if he had eaten fewer, any of the other three could have eaten more than the minimum.

Therefore Plato ate seven cakes, Diogenes ate three, Socrates ate two, and Plato ate one.[/spoiler]