Immediately I felt different.

I can’t quite explain how. It was almost as if there was a melody, just beyond the range of hearing, and I could almost hum it. As if the universe itself was whispering in my ears, though I wasn’t sure what it was saying. As if the hidden patterns behind the world were...well, if not quite laid bare, then perhaps their outlines or shadows were a little more visible. 

Why was I here?

The question presented itself with a raw urgency. And the answer was suddenly clear.

To provide entertainment, of course.

But that had an obvious corollary.

A solution to my predicament exists. It isn’t fun to watch a robot slaughter a helpless human. The odds need to be, if not even, then roughly of the same magnitude. The human needs to have a fighting chance.

But the question remained nagging in my mind. Why was I here? Why me?

If they wanted to see a hand-to-hand sword vs saw battle, they could have kidnapped someone from the college football team. No, I must be here because there is a way to win that plays to my strengths.

The universe is giving me hints, I realized. That is what the CHI stat means.

My mind continued, seemingly of its own accord. Elves. Homicidal robots. A gladiatorial arena. This place was very trope-aware. Could I exploit that?

What do you when faced with an artificial intelligence out for your blood?

I stopped running for a moment and shouted. “Does the set of all sets contain itself?”

And -- bless me -- the Dalek stopped, if only for a second before resuming turning in my direction.

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“Invalid question. The definition of a set precludes consideration of the set of all sets.”

It answered! It actually answered! It was the same tin voice that was repeating "Exterminate" earlier, and it seemed to be coming out of a grate in the robot's torso. 

If it had answered yes, my next question would have been to ask whether the set of all sets that are not members of themselves contains itself. It's a doozy, but either answer leads to a contradiction. Unfortunately, the robot didn't take the bait.

All right then, let’s try something else.

“This statement is false.”

“Invalid statement.” This time it did not even pause. “Self-reference prevents assignment of truth value.”

“A million grains of sand is a heap; a heap of sand minus a grain is a heap; therefore one grain of sand is a heap.”

“Sorites paradox detected.” Again, it did not even slow down. “Predicate ‘heap’ has unclear boundaries.”

Okay, so the metal trash can had a reasonable knowledge of philosophy. If I was going to stump it, it was going to be with something it had never encountered before. Something no one would have thought to program into it.

Maybe something a little stupid.

“Not all positive integers are interesting,” I shouted.

This time it did pause. “Correct. The mathematical properties of most natural numbers are not worthy of the processor cycles required to investigate them.”

“So there exists a set of non-interesting positive integers.”

“Premise accepted.”

“But then this same set has a smallest element,” I finished. “Which is interesting?”

The Dalek stopped and I did as well, for I was nearly out of breath.

“The smallest non-interesting positive integer is interesting by virtue of having that property,” it repeated.

Well, fuck.

For a half-a-minute or so we just stood there without either of us saying anything.

“Proof by contradiction accepted. All positive integers are interesting. Extermination cancelled. Resolved: my remaining processor cycles must be dedicated to the study of properties of integers,” it declared, before turning around and wheeling back towards the open gate it came from.

And then the arena was filled once more with the sound of a stampede as seemingly every elf began stomping feet against the floor.