Puzzles,conundrums, riddles and thoughts?

[Sparta]

The answer to the riddle is that Ziggy Stardust is a fellow lurker and/or member at the Straight Dope and has brought unto us the unholy incarnation of the most heated debate present there in recent history. Their server is responding as well as usual right now (i.e. not at all), so I can't link the thread or the article ATM, but IIRC the whole setup is impossible as it creates an infinite feedback loop between the wheel rotational speed and the conveyor belt speed. (For example, if the plane's engines have gotten enough thrust to normally propel the plane forward at 100 mph, the wheels would therefore be spinning opposite at a ground rate of 100 mph, but the conveyor belt would in turn have to go 'backwards' at 100 mph as well, so the wheels would actually have to be going 200 mph. Since the wheels would always have to be spinning twice as fast as any other component (or at the combined rate of speed of the conveyor belt and the airplane's theoretical speed), the whole setup is impossible. If you ignore that, the plane would take off independent of the conveyor belt, as the thrust is being created via the jet engines and therefore wheel speed is irrelevant, but with the stipulated setup, I believe that the entire situation is an impossibility.

And now that I've typed up my clumsy response, the server hamsters are on the move, and here are the better responses by the Perfect Master Cecil Adams:

Article One
Article Two
(Disclaimer: I haven't read those in quite a while, but I think that what I had said above should loosely correlate with the statements in the articles.)

Here I thought things were already getting ugly as I was looking through scores of useless, lame, and repetitious 'difficult brain teasers' to attempt to find one worthy of this thread, and then I come back here and see the infamous plane-on-a-treadmill dilemma ...

(and once again, my rambling typing style leaves me about a half-dozen posts behind everyone else ...)

 

[Sidhe]

OK was I right in the first place or not?

If I was let Brenan have a go anyway, he hasn't had one yet AFAIK.

 

[Riffraff]

Is the plane moving relative to the air? If the answer is no, then you have a grounded plane because there is no lift. That site makes the same irrelevant argument wrt the wheels. The wheels are not the issue.

but the airplane does move relative to the air - why wouldn't it? It's kinda silly to assume that the friction of the wheels with the conveyer belt would be able to match the forward thrust of the engines. It is actually negligable.

 

[nonconformist]

Is the plane moving relative to the air? If the answer is no, then you have a grounded plane because there is no lift. That site makes the same irrelevant argument wrt the wheels. The wheels are not the issue.

That's fully my opinion, since the link I gave seems only to confuse me.
I would think that what he says about the wheels not being material to he airplane would be the same as the plane jsut hovering over the treadmill

 

[brennan]

Yes, I see what you are getting at.

Noncom, what he is saying is that if you accelerate the plane on the conveyor that it will move forward regardless of what the conveyor is doing. ie, you read into the question that the plane is stationary, but this will not be the case.

 

[nonconformist]

but the airplane does move relative to the air - why wouldn't it? It's kinda silly to assume that the friction of the wheels with the conveyer belt would be able to match the forward thrust of the engines. It is actually negligable.

Because of the treadmill, the plane is not moving relative to the ground. It would then follow that, unless there was a hurricane, or a big fan or something, the air would also be stationary.

 

[Taliesin]

WANT MORE RIDDLES!

 

[Sparta]

WANT MORE RIDDLES!

Who can turn that down?

This is lame, but the best I was able to come across previously that wasn't already covered in some form (or incredibly easy; this is easy, but not necessarily instantly so I hope), although it may have been in previous riddle threads here:

You are in a room with three switches, each of which individually controls a light bulb in a separate room that you cannot in any way see from your current room. You are only allowed to enter the second room with the light bulbs once. If all light bulbs are currently off, how can you determine which switch controls which light bulb instantly upon entering the second room?

 

[Perfection]

http://www.esa.int/SPECIALS/Cassini-Huygens/SEM1531DU8E_0.html

You should verify your opinions before you make yourself look like a fool. Now if we may proceed without interruptions from pedants.

That's as much a methane volcano as volcanoes on Earth are carbon dioxide volcanoes. Honestly, your grasping at straws here, just admit that you were clueless and had no business making riddles about planetology.

 

[Taliesin]

You leave switch 1 on for five minutes, then flick it off, flick switch 2 on, and hurry into the room. The light will be off and hot, on, or off and cool.

 

[Riffraff]

That's as much a methane volcano as volcanoes on Earth are carbon dioxide volcanoes.

it's actually even less than that...

 

[brennan]

That's as much a methane volcano as volcanoes on Earth are carbon dioxide volcanoes. Honestly, your grasping at straws here, just admit that you were clueless and had no business making riddles about planetology.

He quotes a European Space Agency site describing them as methane volcanoes. Why don't you take the ESA to task and cut out the personal attacks.

 

[Taliesin]

OK, so here's a riddle to which I don't have the answer. I'm trying to work it out, and maybe we can do this one collaboratively.


A man says he's going to give you some money. He puts an amount into two different envelopes, and tells you that one envelope has twice as much as the other. You pick one randomly, and it contains $20. The man says you may now keep that $20, or exchange it for the other (unopened envelope). Assuming risk management isn't an issue (i.e. it's purely a question of expected return), what do you do?

It seems you should ask to exchange. The other envelope contains either $10 or $40, so you have an equal chance of losing $10 or gaining $20. That gives you an expected gain of $5.

But then, and here's the riddle, imagine that you haven't opened your envelope yet. Regardless of what amount x is in it, your expected gain by switching seems to be (2x - 0.5x) / 2. But that's absurd, because it means that whichever envelope you have, you should take the other.

What is wrong with the above reasoning?

 

[brennan]

Either way you have a quantity X. So if you swap you either lose X/2 or gain X. I think the trick is that you are not starting with nothing. If you had to pick an envelope at random then you are starting at 0 and either gaining X or 2X. In this scenario you do not have the same start point. It's similar to monty hall, in that some of the variables are hidden by the circumstances.

 

[nonconformist]

OK, so here's a riddle to which I don't have the answer. I'm trying to work it out, and maybe we can do this one collaboratively.


A man says he's going to give you some money. He puts an amount into two different envelopes, and tells you that one envelope has twice as much as the other. You pick one randomly, and it contains $20. The man says you may now keep that $20, or exchange it for the other (unopened envelope). Assuming risk management isn't an issue (i.e. it's purely a question of expected return), what do you do?

It seems you should ask to exchange. The other envelope contains either $10 or $40, so you have an equal chance of losing $10 or gaining $20. That gives you an expected gain of $5.

But then, and here's the riddle, imagine that you haven't opened your envelope yet. Regardless of what amount x is in it, your expected gain by switching seems to be (2x - 0.5x) / 2. But that's absurd, because it means that whichever envelope you have, you should take the other.

What is wrong with the above reasoning?

Is it classic Monty Hall?
As in, it's not a 1/2 chance, but a 1/3 chance?

 

[Perfection]

He quotes a European Space Agency site describing them as methane volcanoes. Why don't you take the ESA to task and cut out the personal attacks.

He misquotes the ESA! It's an ice volcano that emits some methane, just like a volcano on Earth is a rock volcano that emits some CO2. You don't call our volcanoes CO2 volcanoes, do you? You're not gonna be standing outside the erupting volcano going "hey, look at all the methane", you're going to be looking at the ice and water!

 

[El_Machinae]

A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?

http://forum.physorg.com/index.php?showtopic=2417

I invite people to click the link above, and see what hard-headedness can result in. You mostly need to note the size of the thread.

 

[Sparta]

I'd come across the same thing while looking for a decent one to post here, but now I can't seem to find the same page again ...

I'd be inclined to think it is akin to what brennan and nonconformist are saying, in that maybe it is just a matter of perspective somehow. I may be missing something, but I think that without knowing which envelope you have, you would always be correct in switching, a la the Monty Hall problem. FWIW, IIRC, the site I'd glimpsed briefly in my search seemed to adopt a "don't care" stance toward the problem prior to opening one envelope or the other (not sure if that helps at all though).


... 468 pages!!

 

[Ziggy Stardust]

468 pages indeed! Wow.

About the enveloppes, before you open one, you have an expected value of (x+2x)/2 = 1.5 X, the average.

At this point switching will be a neutral gamble (+0.5X or -0.5X) since you don't know what you have. All you know is what to expect: 1.5X. That changes when you know one of the values in one enveloppe.

edit: By the way, I don't lurk Straight Dope Heard of it though. But the plane does take off

Is the plane moving relative to the air? If the answer is no, then you have a grounded plane because there is no lift. That site makes the same irrelevant argument wrt the wheels. The wheels are not the issue.

It looks like you are making the case for the plane not being stationary, am I right?

Yep. If the plane is stationary it's paperweight. But the thrust causes acceleration, not mechenical force on the driveshaft or the wheels. If you'd do this with a car you'd get nowhere (*and would be impossible to set up).

Since you can make a trolley go 5 mph on a conveyorbelt going 5 mph in the oposite direction by pushing it m(just as the jet engines would push against the air) the plane will take off.

 

[brennan]

468 pages indeed! Wow.

Yep. If the plane is stationary it's paperweight. But the thrust causes acceleration, not mechenical force on the driveshaft or the wheels. If you'd do this with a car you'd get nowhere (*and would be impossible to set up).

Since you can make a trolley go 5 mph on a conveyorbelt going 5 mph in the oposite direction by pushing it m(just as the jet engines would push against the air) the plane will take off.

Yeah I get it. In rather less than 468 pages. Do I get a prize?