A dilemma is when there are only two possibilities and both of them are impossible. That is a dilemma.

13 seconds sound clip from the The Fall of the Roman Empire (1964) movie soundboard.

You can hear this line at 00:31:49.213 in the Blu-ray version of the movie.

Quote context

[...]

- Caesar was just telling me I should change.

- Oh, father thinks too much. There is much for a Roman to think of these days.

- Why Livius, for a moment that honest warrior's face of yours took on the philosopher's look.

- Let's not think, let's drink.

- As in the old days?

- As in the old days.

- Did you study logic? Do you know what a dilemma is?

- A dilemma is when there are only two possibilities and both of them are impossible. That is a dilemma.

- Drink with me. Now drink with me. Drink with me!

- I'm Caesar's son, I could have you burned alive!

- Why Livius... My friend. My brother.

- Something is struggling you, isn't it?

[...]