Counter intuitive puzzle

[Krynn72]

I was just reading an article on some game design stuff, and the author brought up the following puzzle.

The Monty Hall 3-door puzzle: In the popular 60's - 70's game show, Let's Make A Deal, host Monty Hall would give the final contestant a chance to pick one of three showcase doors. He tells the contestant that behind one door is the big prize (maybe a car), behind another door is a runner-up prize (maybe a TV set), and behind the final door is a booby prize (often a farm animal, like a donkey). So, the contestant picks a door, let's say door #1. Monty doesn't open that door right away -- instead he builds excitement by first opening one of the two un-picked doors. (It's important to know that Monty knows what's behind each of the three doors. And he'll never open the door with the big prize during this stage.) Let's say Monty opens the door with the runner-up prize, revealing a TV set. That leaves two unopened doors, one with the big prize and one with the booby prize.

Now comes the fun part: Monty turns to the contestant, and says, "Well, there are two doors left, and so far so good -- you know the car is either behind the door you picked, or the door you didn't pick. Tell ya what...do you still feel like you made the right choice? If not, I'll give you a chance to switch your pick to the other unopened showcase door. Whachya wanna do?"

So, if you're that contestant, do you stick with the door you originally picked, or do you switch? (At some point I'll post the answer in the comments section.)

And in the comments, after some people posted what the answer was, he said that it was indeed best to switch your choice. The probability, he says, for your door still being the door with the best prize is still 33.333% while the probability for the other door is 66.666%. This just proves to me how bad I am at math, because I don't get how thats the case, and that its not then 50/50.

He then says,

This time there are a MILLION doors, and just one prize. You pick a door, and then KAPOW! Monty hurls open 999,998 of the other doors, leaving door #36,971 suspiciously closed. NOW do you stick with your original choice, or switch?

And someone else comments that they use the million door example to show people who think its 50/50 that its not.

But I still dont get....

Oops, I get it now haha. Guess I just needed to write it out to force me to think about it a bit more.

Anways, Lets get a whole thread of these unintuitive puzzles going. They're pretty fun.

Heres another one.

A couple has two kids, and they happen to mention that one of them is a girl and plays soccer. What are the odds that their other kid is also a girl?

Also, if an airplane is on a treadmill...

 

[Acepilotf14]

If you attach a piece of toast with peanut butter spread on one side to the back of a cat, which side will hit the floor?

 

[xcellerate]

yea the problem is difficult for some people because they don't realize the odds of the door you picked don't change from 1/3 simply because you opened another door.

the treadmill/airplane one is the stupidest "riddle" on the planet. I still can't believe the number of people who think a plane can't take off.

 

[63]

http://en.wikipedia.org/wiki/Monty_Hall_problem

A couple has two kids, and they happen to mention that one of them is a girl and plays soccer. What are the odds that their other kid is also a girl?

1 millions.

 

[VirusType2]

A couple has two kids, and they happen to mention that one of them is a girl and plays soccer. What are the odds that their other kid is also a girl?

Zero; if one of them is a girl, then the other one is not.

 

[xcellerate]

Zero; if one of them is a girl, then the other one is not.

well one of them is a girl AND plays soccer, the other could be a girl who doesn't play soccer.

 

[VirusType2]

It could if you don't know how to stream statements in a logical way.

This is appropriate: I've got 2 girls. One of them plays soccer.

Not: I've got 2 kids. One of them is a girl and plays soccer. The other is a girl and ... (doesn't play soccer?)

 

[Acepilotf14]

well one of them is a girl AND plays soccer, the other could be a girl who doesn't play soccer.

If the other wasn't a boy, they would've said 'We've got two girls and one plays soccer'.

 

[VirusType2]

I think xcellerate is just saying it's possible and I won't deny that. But I think this is a reading comprehension thing, not a possibility thing. Otherwise, why even pose it as a word problem? It's possible if it's intentionally misleading.

 

[huntingbear]

i swear to god my mind is blown by the people who think the airplane won't take off.....seriously....

 

[MJ12]

If I've got one question, man, tell me who's next.

 

[StarBob]

yea the problem is difficult for some people because they don't realize the odds of the door you picked don't change from 1/3 simply because you opened another door.

the treadmill/airplane one is the stupidest "riddle" on the planet. I still can't believe the number of people who think a plane can't take off.

I still don't understand the treadmill thing. I know there's a thread somewhere on it, but knowing the principles of aerodynamics and fixed wing flight.... I could just assume the people saying it does take off are just playing around for fun.

I don't like puzzles that are a matter of interpreting words... because that's way too subjective.

Edit: oh I read that wrong, I thought that you got to open the door and then had the option to switch. I see now that you choose a door, then he shows you a door, random door, then you can switch or not switch. You never know what's behind the door you pick so it's still 1/3.

Oh well... the airplane thing doesn't work for me.

 

[Krynn72]

Zero; if one of them is a girl, then the other one is not.

Haha, I don't think its intended to be interpreted as trick of phrasing. Its supposed to be a probability question.

@Starbob: But the probability DOES change. Its no longer 33% each. Once he removes one of the false doors, the probability that your chosen door has the car stays at 33%, while the probability that the other remaining door has it goes to 67%

 

[15357]

yea the problem is difficult for some people because they don't realize the odds of the door you picked don't change from 1/3 simply because you opened another door.

the treadmill/airplane one is the stupidest "riddle" on the planet. I still can't believe the number of people who think a plane can't take off.

I know that a rotary aircraft will take off, because it forces the air under the wings without the need to gain airspeed, but what about a jet with its engines situated at the back?

 

[xcellerate]

I still don't understand the treadmill thing. I know there's a thread somewhere on it, but knowing the principles of aerodynamics and fixed wing flight.... I could just assume the people saying it does take off are just playing around for fun.

The treadmill thing is misleading. Within reason, the wheels on planes are not important, even the surface they're on isn't important, and in the right conditions planes don't even need a surface to take off. A plane can take off on concrete, ice, snow, dirt, water, and if you dropped it straight down from a hot air balloon (given enough time) it would start to fly.

The point is, unlike a car, wheels are fairly unimportant to move a plane forward. Imagine a rocket car on a treadmill. If the treadmill moves backwards at the same speed the car's wheels move forward, the car stands still. But when the car activates that rocket on it's roof, do you still think the car will stand still? Or will it launch forward?

I know that a rotary aircraft will take off, because it forces the air under the wings without the need to gain airspeed, but what about a jet with its engines situated at the back?

prop planes don't fly by forcing air under the wings. The prop, moves the plane forward just like a turbine. pusher craft action:

 

[StarBob]

Ah I see. I just don't get how the probability is different for your chosen door or the remaining non-chosen door. Since you don't know what is behind either... it seems they'd both be 67. Maybe I have to look at that wiki again when it's not so late.

Also, I'm pretty sure a propeller driven craft wouldn't move enough air surface (though it would be at sufficient speed) to lift the full surface of the wings. Propellers move a column of air at high speed directly around them, wings need their entire surface to be moving across the air to generate lift.

I mean this seems simple to me. If I'm running on a treadmill I don't feel air hitting me in the face. If I was running 200 mph I wouldn't feel air hitting me in the face. Something has to be moving under and over the wings to generate lift, otherwise it would just be rolling along at 200 mph or infinite mph.

Edit: Yes if you activate the rocket on the car and it is facing in the the opposite direction of the treadmill... and the treadmill maintains the speed that the rocket increases... then yes it will still be on the treadmill. And in all of the conditions where a plane takes off, the air has to be moving over and under the wings -

If no air moves, this never happens and there is no lift and thus no flight.

 

[15357]

The treadmill thing is misleading. Within reason, the wheels on planes are not important, even the surface they're on isn't important, and in the right conditions planes don't even need a surface to take off. A plane can take off on concrete, ice, snow, dirt, water, and if you dropped it straight down from a hot air balloon (given enough time) it would start to fly.

The point is, unlike a car, wheels are fairly unimportant to move a plane forward. Imagine a rocket car on a treadmill. If the treadmill moves backwards at the same speed the car's wheels move forward, the car stands still. But when the car activates that rocket on it's roof, do you still think the car will stand still? Or will it launch forward?

I understand that if the force is directed upward by thrust, the treadmill will not matter at all for the aircraft will move forward, and therby gain airspeed required for takeoff.

However, I thought that the point of the question was that the airplane was fixed on the treadmill, and thereby be fixed onto the surface, and basically the question asked if an airplane would be able to generate upwards thrust own its own without the need for airspeed? (In which the answer is no)

I mean this seems simple to me. If I'm running on a treadmill I don't feel air hitting me in the face. If I was running 200 mph I wouldn't feel air hitting me in the face. Something has to be moving under and over the wings to generate lift, otherwise it would just be rolling along at 200 mph or infinite mph.

What he said.

EDIT: @ xcellerate: I know how airplanes work, but I thought the purpose of the treadmill was to ensure that the airplane did not gain airspeed, and therefore would require upwards thrust by some other means?

 

[Bob_Marley]

I know that a rotary aircraft will take off, because it forces the air under the wings without the need to gain airspeed, but what about a jet with its engines situated at the back?

It'd still work - the engines don't power the wheels. The aircraft would still be able to reach take off speed but the wheels would simply turn at twice the speed the aircraft is moving foreward.

 

[15357]

It'd still work - the engines don't power the wheels. The aircraft would still be able to reach take off speed but the wheels would simply turn at twice the speed the aircraft is moving foreward.

Again, I thought gravity would force the airplane upon the treadmill so that it wouldn't move? I mean, what's the purpose of the treadmill then?

 

[StarBob]

It'd still work - the engines don't power the wheels. The aircraft would still be able to reach take off speed but the wheels would simply turn at twice the speed the aircraft is moving foreward.

The plane would reach takeoff speed.... let's say 150 mph... but it would still be sitting in one particular space without air moving over the wings generating lift. Lift is the only thing that makes the plane take off. It doesn't matter how fast the wheels spin or if it slides or anything really. As long as - from wingtip to wingtip - no fluid is going over and under the wings - it will not take off.

Edit: Also, while the engines don't power the wheels, they certainly don't power the air that makes the plane fly. The move a column of air that propels the plane forward. Like xcellerate said, this column of air is not significant enough to produce lift. The only way it could ever work is if the engine were so powerful that it could be tilted skyward and lift the plane under the same principles of a helicopter.

 

[15357]

The plane would reach takeoff speed.... let's say 150 mph... but it would still be sitting in one particular space without air moving over the wings generating lift. Lift is the only thing that makes the plane take off. It doesn't matter how fast the wheels spin or if it slides or anything really. As long as - from wingtip to wingtip - no fluid is going over and under the wings - it will not take off.

Ok, you be me for now, you put it in better words then I do.

 

[xcellerate]

However, I thought that the point of the question was that the airplane was fixed on the treadmill, and thereby be fixed onto the surface

If you're strapping it down then it doesn't matter wtf is on the treadmill. With big enough straps nothing will move forward.

If no air moves, this never happens and there is no lift and thus no flight.

But air does move over the wings!

The prop/turbine/rocket moves the plane forward along the treadmill, moving air over it's wings, until it eventually takes off.

edit: imagine a treadmill 10 miles long, there would be plenty of room to take off...unless of course you've strapped it down with diamondillium cables.

 

[StarBob]

If you're strapping it down then it doesn't matter wtf is on the treadmill. With big enough straps nothing will move forward.



But air does move over the wings!

The prop/turbine/rocket moves the plane forward along the treadmill, moving air over it's wings, until it eventually takes off.

That's the fundamental flaw. Air does not move over the treadmill. The treadmill is in place, the plane is in place, the action of the treadmill is only to move the surface, no air whatsoever. If the plane is stationary and the treadmill is stationary - where is the moving air?

 

[xcellerate]

why would a plane stay stationary when it's engines are at full thrust?

 

[15357]

If you're strapping it down then it doesn't matter wtf is on the treadmill. With big enough straps nothing will move forward.



But air does move over the wings!

The prop/turbine/rocket moves the plane forward along the treadmill, moving air over it's wings, until it eventually takes off.

That's what I don't understand. I mean, if you're going to be like that, why do you have a treadmill? I mean, how does the airplane move forward, without the lift generated to ensure that the wheels have reduced friction upon the treadmill, and therefore is able to move forward from the thrust generated by its engines, despite the backwards motion of the treadmill?

Ok, this is what I'm understanding here:

Wheels - don't matter.
Plane is Jumbo Jet
Gravity pulls Jumbo Jet down onto treadmill
the wheels' only function is to reduce friction with the surface of the treadmill
engines push the airplane forward, but the treadmill pushes it back, resulting in a combined force of 0
no movement = no lift

why would a plane stay stationary when it's engines are at full thrust?

Because it's not moving? Imagine a plane with no wings.

 

[kineaesth]

edit: imagine a treadmill 10 miles long, there would be plenty of room to take off...unless of course you've strapped it down with diamondillium cables.

And then xcellerate was confused.

The idea is that the treadmill moves in the opposite direction to the plane, at the same speed, and thus the plane remains stationary, even with its engines at full-throttle.

edit: OR DOES IT

 

[StarBob]

why would a plane stay stationary when it's engines are at full thrust?

Because the motion is only relative to the surface of the treadmill, not the air.

Really the best way to experience this is to run on a treadmill, then run outside. On the treadmill, no matter if you're walking or sprinting, you will not encounter air currents similar to the same action in actual locomotion.

If you sprint at 20 mph in still air, the air going by you is 20mph. You will feel it as you would a 20mph wind.

If you sprint at 20mph on a treadmill in still air, you will feel no air movement aside from the general movement of your body in the running motion. It will not be 20mph.

Relative to the air, which is the necessity of flight, the plane will be stationary as long as the treadmill does not allow it to move forward relative to the air.

 

[xcellerate]

engines push the airplane forward, but the treadmill pushes it back, resulting in a combined force of 0

That's the problem, you're assuming the bearing friction is so great that 35,000lbs of thrust can't over come it. Seems a bit unlikely.

If you sprint at 20mph on a treadmill in still air, you will feel no air movement aside from the general movement of your body in the running motion. It will not be 20mph.

You're forgetting I'm using the treadmill's moving surface for thrust, however the plane uses the air for thrust. Air doesn't have to be moving to generate thrust. The plane uses this thrust to then generate lift.

it's true I can't move forward if the treadmill keeps moving backwards, but if I had a rocketpack, I'd move forward regardless of what the treadmill was doing.

 

[AJ Rimmer]

Relative to the air, which is the necessity of flight, the plane will be stationary as long as the treadmill does not allow it to move forward relative to the air.

Which it will, because the propeller will push the plane through the stationary air, ignoring the effin' treadmill.

OR DOES IT

Well no, no it doesn't.

 

[15357]

That's the problem, you're assuming the bearing friction is so great that 35,000lbs of thrust can't over come it. Seems a bit unlikely.

I'm not sure I get what you mean.

Automobiles accelerate because the contact pad on the tire exerts a force on the ground, and the ground therefore exerts a reactive force on the tire.

Airplanes, I understand do not work like that: their engines exert a force upon not the ground, but something else.

Wait, actually I kinda do get it now. The plane does move. And therfore is able to achieve the speed required for takeoff!


Thank you HL2.net for saving me from ignorace.

 

[kineaesth]

The secret answer is this - the wheels rotate on their own, they are not driven by anything. If the plane was turned off and the treadmill (we are assuming it is flat) was turned on, the slight friction of the wheels would cause the plane to move with the treadmill. If the pilot puts just enough power to the engine to overcome this initial friction, the treadmill could be moving at 100,000 mph and the plane would happily be trundling along with only 1% of it's power. (this is hypothetical. Hypothetically, the wheels won't come apart.) all the pilot then needs to do is increase power to above the level needed to beat the friction from the wheels, and the plane will move forward.

 

[15357]

The secret answer is this - the wheels rotate on their own, they are not driven by anything. If the plane was turned off and the treadmill (we are assuming it is flat) was turned on, the slight friction of the wheels would cause the plane to move with the treadmill. If the pilot puts just enough power to the engine to overcome this initial friction, the treadmill could be moving at 100,000 mph and the plane would happily be trundling along with only 1% of it's power. (this is hypothetical. Hypothetically, the wheels won't come apart.) all the pilot then needs to do is increase power to above the level needed to beat the friction from the wheels, and the plane will move forward.

Yeah, I conducted a thought experiment on my own:

You have a treadmill, running at a huge speed.

You have a model glider with a string attached to the front

You pull it, and the model glider will move forward, but the wheels will spin at a speed greater than the treadmill.

 

[xcellerate]

You pull it, and the model glider will move forward, but the wheels will spin at a speed greater than the treadmill.

 

[15357]

I guess my downfall was assuming that the wheels would have something to do with the speed.

 

[Bob_Marley]

The plane would reach takeoff speed.... let's say 150 mph... but it would still be sitting in one particular space without air moving over the wings generating lift. Lift is the only thing that makes the plane take off. It doesn't matter how fast the wheels spin or if it slides or anything really. As long as - from wingtip to wingtip - no fluid is going over and under the wings - it will not take off.

Edit: Also, while the engines don't power the wheels, they certainly don't power the air that makes the plane fly. The move a column of air that propels the plane forward. Like xcellerate said, this column of air is not significant enough to produce lift. The only way it could ever work is if the engine were so powerful that it could be tilted skyward and lift the plane under the same principles of a helicopter.

You're a mong.

Right, take off speed is 150 miles per hour. The plane is traveling foreward along the treadmill at 150 miles per hour but its wheels are spinning at 300 miles per hour (ie the treadmill matches the speed at which the aircraft is being powered to, 150mph, but as the wheels rotate freely they simply rotate at double the speed, as the plane is moving foreward at 150mph and the treadmill is moving backward at 150mph), so the air moves over the wings at the requisit speed and the aircraft takes off.

 

[VirusType2]

That's the fundamental flaw. Air does not move over the treadmill. The treadmill is in place, the plane is in place, the action of the treadmill is only to move the surface, no air whatsoever. If the plane is stationary and the treadmill is stationary - where is the moving air?

I came here late, so I'm sure this has been answered by now, but this is driving me crazy.

The treadmill is long, its spinning at 100MPH, say.

The airplane pulls air. The wheels are free rolling, it doesn't matter how fast the wheels spin. So, by the time the plane takes off, the wheels will be spinning at 160 mph, while the plane is traveling at only 60 MPH.

so basically, all the treadmill can do is force the wheels to spin faster, which has no bearing on how fast the plane is traveling, since it propels itself with air.

 

[StarBob]

I came here late, so I'm sure this has been answered by now, but this is driving me crazy.

The treadmill is long, its spinning at 100MPH, say.

The airplane pulls air. The wheels are free rolling, it doesn't matter how fast the wheels spin. So, by the time the plane takes off, the wheels will be spinning at 160 mph, while the plane is traveling at only 60 MPH.

so basically, all the treadmill can do is force the wheels to spin faster, which has no bearing on how fast the plane is traveling, since it propels itself with air.

Well yeah obviously if the plane is going faster than the treadmill and it is sufficient length of a runway for takeoff then, yeah it will take off. I thought we were talking about the idea was that the treadmill would increase equal to the plane-perceived velocity (the wheel velocity). The problem here is that as long as there's sufficient gravity there will be friction between the surface and the wheels. I don't think there's an aircraft that could hold up to the power necessary to attain the speed for takeoff in those conditions.

I understand what you're saying though. If I was wearing rollerskates and standing on a treadmill, as long as I had sufficient force keeping me moving forward I would stay in place. The thing is, this still has the hypothetical aspects of wheels that can sustain (without any calculations) twice the force of a plane's maximum takeoff speed as well as the ability to produce thrust much greater than what is normally required for it to take off.

Another issue here is what the speed of the treadmill will be. Since the only thing determining wheel speed is how fast the treadmill is going, then it would increase to infinite proportions (if we're still using hypotheticals) as the plane approaches the critical point where it overcomes the friction of plane to wheels and wheels to surface. With it moving faster it would increase the friction of the wheels to the point there could be no structure to withstand it.

For instance, the pilot is at 5% throttle to compensate for standard friction of wheels and treadmill. He stays in place going 10-20 mph or whatever at his wheels. He increases to 100% and begins to move forward on the treadmill-runway, but as he does the speed is exponentially increasing to compensate for his forward movement, never able to catch up, but increasing nonetheless. While he is accellerating to 150mph air speed down 3000 feet of runway, the ground speed would have been increasing well past that in effort to overcome the forward motion. I figure somewhere around 400 mph or so, the tires would blow. Whether this would happen or not would depend on rate at which the treadmill is capable of accellerating.

edit:
a = wheel velocity
b = treadmill velocity

While wheelonsurface = true
{
Roll()
}
while a > b
{
a++
}

That's how I would program the treadmill to function. So as long as the A is greater than B (which will be at any point that it the plane begins to move forward) A wil increase. The plane will still move forward, but A will be increasing as fast as the mechanical operations would let it.

 

[Higlac]

Oh look, it's this thread again.

The plane would take off. The only reason it wouldn't is if the wheels provide enough friction to keep the plane from reaching takeoff speed.

 

[Vegeta897]

You all are ****ing retards and I'm seriously disappointed that you've all forgotten the epic thread about the airplane in the past, specifically the outcome and final conclusion. The existence of that thread should act as an unwritten rule on hl2.net that this topic is never to be discussed again.

Please refer to my sig, "My Favorite Thread"

 

[StarBob]

Yes Vegeta.... we've all been sitting around here since 2006 reading every single thread and hoping we don't disappoint you...