Behold, mortals, I am the superintelligence Omega.
I can, by examining you for just a few short minutes, form such a good model of your personality that I can predict your actions.
I have, out of your sight, two boxes. One is opaque, one is transparent.
I shall place in the transparent box £1000.
If I believe that you will not take the transparent box, then I shall place £1,000,000 in the opaque box.
But if I believe that you will take the transparent box, then I shall place nothing inside the opaque box.
After we talk, I shall place before you the two locked boxes.
Once I have done this, I will not interfere. You may take either or both with you.
Once you have left my domain and the door has closed forever behind you, the locks on the boxes will open. The contents, exactly as I placed them before you made your choice, will be my gift to you.
So spoke Omega, the godlike alien who sometimes appears to destitute travellers in their hour of need.
Many people have taken his test, and it seems that Omega is always right. Those who take only the opaque box find themselves rich. Those who take both find themselves with their expenses paid, but not nearly as happy as you'd expect people who've just been given £1000 by a generous alien god to be.
You have now had your interview, and Omega is gone. Before you are two boxes.
Omega has promised that it doesn't matter what you do. What he put in the boxes ten minutes ago is fixed and he won't change it or use any sleight of hand or trickery.
You'd be a fool not to take the opaque box, which may or may not contain a fortune.
But do you take the transparent one, which definitely does contain £1000 that you can see, the alien's gift to you?
Without it, you will not be able to pay your fare home, and you will die on this trackless desert planet, friendless and alone.
Everyone agrees that the answer to this question is obvious.
The problem is that some people say that it's obvious that you should take one box, and some people say that it's obvious that you should take both.
I actually seem to think that both answers are obvious, which really does make me wonder what I mean by obvious.