Maggie's Farm

I have enjoyed logic puzzles like this since highschool, and have found that the discussions by intelligent people debating them is more valuable than the problems themselves. This is because there is usually either insufficient information or self-contradiction hidden in the problem, which people attempt to get around by making extra assumptions. It is fascinating to note what extra assumptions people add in - rules that they believe "should be" there.

In this instance we have posited an omniscient alien. That is one of the few "rules" in this closed system. That rule is already an impossibility - it is an artificially set-up situation which cannot exist. If we go along with the game and accept that rule as being operative in the system, then no further discussion is meaningful. You are not deciding anything, as the alien already knows your decision. All mental pictures of yourself sitting in front of boxes thinking about what you might do are deceptions.

We treat the choice between boxes as a real choice because that is something that looks like real life, and real decisions. We often make choices about things. But this part of the problem is an illusion, a realistic-looking event set within an impossible one. Like the grandfather paradox or Russell's paradox, a homely, normal-looking event is placed in an impossibility to trick the mind into treating it as something possible.

As an example: If you had no hat, what hat would you have? Once we have granted the initial rule - No Hat - further discussion is meaningless. It does not become meaningful just because we are talking about everyday objects like hats.