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?

Comments

[jackoutofthebox.livejournal.com]

1) The plane needs air to rush under the wing, it's not about distance. Technically if an airplane was on top of Mt Washington and the windspeed gets high enough, the plane could take off vertically.

2) You never stated you couldn't open the door chosen/ open it and if it's a goat, you can choose the remaining door for the car.

3) The flaw in his logic was getting into this pit in the first place.

[corruptedjasper.livejournal.com]

No, Switch (unless you prefer the goat), and It Was Unexpected, Wasn't It?

[dolston.livejournal.com]

1 - no
2 - pick a door and don't change your pick
3 - I need to finish my coffee and eat before I think that hard.

[jaffa-tamarin.livejournal.com]

I think the treadmill only stops the plane taking off if it goes fast enough to destroy the landing gear when the wheels overheat. But to be on the safe side, I'm using a Harrier Jump Jet.

[flemco.livejournal.com]

1) GOD DAMMIT YOU MOTHERFUCKER
YES, YES, A THOUSAND TIMES YES THE PLANE WILL BOTH MOVE FORWARD AND TAKE OFF GOD DAMMIT REGARDLESS OF WHETHER IT'S ON A CONVEYOR BELT, A GIANT LAKEBED COVERED IN MAYO OR ROLLING DOWN THE STREET SMOKIN' INDO SIPPIN ON GIN AN JUICE LAID BACK WITH ITS MIND ON ITS MONEY AND ITS MONEY ON ITS MIND

[argaive.livejournal.com]

Pop Quiz:
Unlike a person walking or an automobile driven by its wheels, an airplane's engines don't act against the surface it rests on when not in flight, so the treadmill will have no effect once the airplane is moving under its own power.

Bonus points:
At that point the odds are fifty/fifty, so you can't really do anything to change your odds; that's as good as they'll get.

Extra bonus points:
He was right about the fifth door, but he carried that logic too far. Besides which, if the King said there was a lion and he couldn't lie, then there had to be a lion.

How'd I do?

A.

[leighdb.livejournal.com]

1. Not Going There Again. 116 comments and I still don't really get it.

2. Ask the host to open one of the other two doors before choosing. (Hey, you didn't specify that you have to make the choice without opening either of the other doors.)

3. I suck at logic as well as physics! But, I think the flaw here is that the only door the lion could not have been behind and still been unexpected was the fifth door, for exactly the reasons the man says.

However, after the man had made the logical deduction that followed (that therefore the lion also couldn't be behind the fourth door, or third, etc.), that's where it falls down, because to find that there was a lion behind one of the doors after all would of course have been totally unexpected.

[lonebear.livejournal.com]

1 - proven. IF the wheels were powered then the treadmill would matter. However, since the power for an airplane has nothing to do with what the wheels are doing it does take off.

[silmaril.livejournal.com]

You cannot hold the plane down!

[psyco-path.livejournal.com]

The treadmill needs to be on a merry go round

I would rather the goat.

Completely unexpected would be a hippogriff eating him.

[theweaselking.livejournal.com]

Whatever door you open, you keep. So if you open your choice and it's a goat, you get a goat.

[theweaselking.livejournal.com]

The question has nothing to do with preferring cars or goats, and everything to do with maximising your chances to get the car.

I specifically worded it that way, because I know there are furries and scandahoovians who read this.

[jagash.livejournal.com]

1) Agreed, however without crossing any distance it is unlikely that there will be any appreciable wind. Unless the treadmill moves fast enough to cause a major wind current, not going to lift off.

[ceramufary.livejournal.com]

1) Plane needs air speed! If the treadmill keeps the plane in place, plane can't take off. What a waste!

2) Always switch! First choice was a 1/3 chance, but after the choices are whittled down to two doors, switching means changing to a 1/2 chance. But I /know/ that one previously, and still can't get my head around it. Once the goat-door is opened, isn't your first choice now a 1/2 chance too? It is madness.

[scifantasy.livejournal.com]

You got the first one right.

The second one, wrong...Wikipedia actually has a pretty good article on the Monty Hall problem (as this one is called), take a look.

The third is right.

[ben-raccoon.livejournal.com]

1) Yes, because the wheels roll freely; airplanes are powered by the jet engines when taking off. This just means the wheels will spin twice as fast when rolling downt he runway.

[jrolsma.livejournal.com]

So you watched Mythbusters this week too?

They explain it as the forward momentum of the plane is caused by the propeller (or jets) pushing air, not the wheels against the pavement. For the ultralight prop plane they used, the wheels moved freely, all forward movement was cause by the prop. And yes, it took off.

[theweaselking.livejournal.com]

The third is *wrong*, actually.

[neobitch.livejournal.com]

1. The treadmill has nothing to do with the plane taking off. A plane's wheels are not powered. The Straight Dope explains this one nicely, for those who have a hard time wrapping their brain around it.

2. There is nothing you can do to improve your odds at this point. It's 50-50.

3. I got nothin'. I'm looking forward to seeing the answer.

[theweaselking.livejournal.com]

Once the goat-door is opened, isn't your first choice now a 1/2 chance too?

No.

Think of it this way: You're getting either the original door you picked, or the best of ALL OTHER DOORS YOU DIDN'T PICK.

Does that help to explain why you're getting better odds switch?

What if the host told you "Okay, you've picked door #1. Now, you need either stick with door #1, or open all the other doors one at a time until you find the car">

[ceramufary.livejournal.com]

Right! That does make sense.

[ceramufary.livejournal.com]

Ohhhhhhhh. *blush!*

[theweaselking.livejournal.com]

1: Mostly Right! The wheels *do* provide the treadmill with a way of moving the plane since they're not frictionless, but they can't stop it unless it goes so fast that the wheels explode.
2: Wrong!
3: Answer coming later, or maybe tomorrow.

[scifantasy.livejournal.com]

Is it? Huh.

[publius1.livejournal.com]

You must assume (1) completely frictionless ball bearings, (2) a treadmill that can go at speeds nearing 200 MPH, and 3) a spherical cow.