Each clue below points to a different four letter word. All four words use the same letters. All answers accepted: Skin torch Keep open? Sit it down. Recent tour?

Airline. Change. River. Slope. Triangle. Discriminant. Particle. Is it just me, or am I starting to sound Greek?

It starts with a thought. There's a cat in me. Put a particle, and it dies. Or so you think. You can't see it, but the states... there are two, both at once. I'll ask you this one time... what am I?

We can play a little game of wits, if you like. If you would think to insult my intelligence, then you have already lost. Nothing looks worse on a person than cruelty and contempt, and my arguments are every bit as good as yours, in any measurable degree. If instead you would compliment me, you shall honor yourself, for kindness carries a dignified air of nobility, and sits well on any who choose to wear it. Whether the game is to be played at all, of course, is up to you.

There are eight in a single elimination event. Start with a size of a container of ice cream or milk. Next a transcendental number followed by a formal ask to provide details. Finish with a continent and things people put on their refrigerator or notepad.