Because aor shouldn't have *all* the fun.

[theweaselking]

Pop quiz:
An airplane is on a gargantuan, infinitely-long treadmill.

The airplane starts it's engines. As soon as it begins to move, the treadmill begins moving in the opposite direction, as fast as you feel like having it go to prevent the plane's takeoff

Will the plane take off anyway?

EDIT: With an infinitely long, arbitrarily fast treadmill, we can also assume that our wheels can handle this arbitrary speed. The tires will not blow and the struts won't melt, no matter how fast those wheels start rolling.

Bonus points:
A game show has three doors. Behind one of them is a new car. Behind the other two are goats.

You're asked to pick one door. WITHOUT OPENING THAT DOOR, the host opens ONE OF THE OTHER TWO DOORS to show you a goat. He then asks you whether you want to keep your original selection, or swap to the last unopened door. You keep whatever is behind the door that you finally decide on.

What should you do to maximise your odds of getting the car?

EDIT: This is a GAME SHOW, people. You don't get to open the doors yourself - Vanna White does that - and she only does it after you tell Regis that yes, that is your final answer and Jeff Foxworthy has mocked you for being dumber than a fifth grader. And you don't get do-overs. Also,the question doesn't care if you prefer goats or not. The question is how to maximise your odds of getting THE CAR, which you can probably sell to buy several goats if that's your thing, but you have to do that after the show.

EXTRA Bonus Points

There is a king who CANNOT LIE.
A man wishes to marry the king's daughter, and is told he may do so if he passes a test.
The test is this: He will be placed in a pit that has five doors, labelled 1 through 5. He will be armed with a spear and a shield.
He must open the doors, one after another, in order, starting from #1.
Behind one of these doors, the king promises there will be a TOTALLY UNEXPECTED LION.
If the man kills the lion, he will be allowed to marry the princess.

So, the man thinks. If he opens the first four doors and there's no lion, then the lion will have to be behind the fifth door. Since he will then know where the lion is, it will not be unexpected. Therefore, the lion cannot be behind the fifth door.

So, the man thinks. If he opens the first three doors and there's no lion, and the lion can't be behind the fifth door, that would mean the lion must be behind the fourth door. And that's not unexpected, so the lion cannot be behind the fourth door.

Similiarly, he realises the lion cannot be behind the third, second, or first door and still be unexpected. Therefore, in order for the king to not be a liar (and the king CANNOT lie), there can't be a lion behind any of the doors at all. And, from a certain point of view, isn't "no lion" a really unexpected kind, under these circumstances?

So:
He confidently strides up to the first door and throws it open. No lion.
He confidently strides up to the second door and throws it open. No lion.
He confidently strides up to the third door and throws it open. No lion.
He confidently strides up to the fourth door and throws it open. Completely unexpectedly, the lion eats him.

What was the flaw in his logic?