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Author Topic: The questions, riddles and puzzles thread  (Read 38020 times)

Kay12

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Re: The questions, riddles and puzzles thread
« Reply #465 on: August 14, 2011, 05:23:04 am »

Actually it works with any mass... a kilogram of light material will weigh as much as a kilogram of a heavy material.

However, if the scales are really sensitive, they could still, depending on the way the feathers are arranged on it, suggest feathers to weigh less as individual feathers may be momentarily lighter because of air currents etc...
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Korgus

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Re: The questions, riddles and puzzles thread
« Reply #466 on: August 14, 2011, 05:29:58 am »

I just looked it up. Feathers are measured in avoirdupois pounds (453g) and gold is measured in troy pounds (373g). So the pound of feathers is heavier if you're not using metric.
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Kay12

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Re: The questions, riddles and puzzles thread
« Reply #467 on: August 14, 2011, 05:45:04 am »

So, the trick question gains additional dimensions in the Imperial world... neat :) Here in metric system that's basically a trick because people instinctively think that gold is of course heavier than feathers in equal quantity... unless it's equal in mass, of course.

I've been studying a lot lately, and I've forgotten all my riddles, except a few classic questions regarding math, logic and computer science.

Is it possible to create an algorithm P, that examines any algorithm and returns true iff that algorithm halts in finite time? (instead of infinite looping, infinite recursion etc...)

Spoiler (click to show/hide)
The reason I posted this is because I recently found a very cool poetic explanation for the problem here.
« Last Edit: August 14, 2011, 05:47:25 am by Kay12 »
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ed boy

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Re: The questions, riddles and puzzles thread
« Reply #468 on: August 28, 2011, 09:46:49 am »

I have a couple more.

A sheet of metal with a circular hole in the middle is heated uniformly. Does the size of the hole increase, decrease, or stay the same?

A rock that is significantly more dense than water is frozen in an ice cube such that the ice cube plus rock is significantly less dense than water. The ice cube is placed in a glass of water, and over time the ice melts. What happens to the water level in the glass? (you do not need to give an exact answer, a rough one will do)

Also, does anybody have any more puzzles that are based of physical situations (as opposed to the logical puzzles that are common here)?
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Il Palazzo

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Re: The questions, riddles and puzzles thread
« Reply #469 on: August 28, 2011, 08:49:54 pm »

A sheet of metal with a circular hole in the middle is heated uniformly. Does the size of the hole increase, decrease, or stay the same?
It increases. I'm not too happy with my explanations though.
Explanation 1:
As the neighbouring molecules in the sheet are being heated up, they start to occupy more volume of space, forcing an increase in the distance between them by a certain amount directly related to the temperature. Any pair of neighbouring molecules will produce the same result, regardless of where they are in the sheet. One can plot a path of pairs of molecules, each pair neighbouring the next, across the sheet to connect any two points therein. By adding the distance increase(either by plotting it all on a cartesian reference plane and adding each pair's contribution to the distance increase along bothe x and y axes, or by relying on simple vector addition techniques known from secondary-ish school mathematics) one can find out that regardless of the shape of the path plotted, and whether or not the path encompassess any holes of whatever shape, the distance between any arbitrarily chosen starting and ending points(molecules) in the path always increases, and in direct, linear proportion to its starting separation distance.
For example, imagine that this is a metal rod, with a gate-like bend in the middle:
__|-|__
It's easy to see that the gap at the bottom of the gate will expand accordingly with the rest of the rod's expansion. It can be extrapolated to any shape and size, as long as there is an unbroken path connecting all the molecules in the material, and that the material is otherwise rigid.

Explanation 2:
Imagine a one molecule-thick ring of metal, corresponding to the rim of the hole in the sheet. It's circumference is πd(d=diameter). It is made up of N molecules, with each molecule occupying L amount of space alongside the lenght of the rim. So, πd0 = N*L. After heating the ring up enough, the molecules now occupy 2L space, so πd1 = N*2L; After simple substitution, we find out that: d1 = 2d0, that is, the diameter must have increased, to accomodate the more voluminous molecules.
We can extrapolate this to any number of additional rings of material, each lying Δd farther than the previous one, where Δd is the distance to the next ring related to the size of a molecule (L) albeit measured in the radial direction:
π(d0+Δd) = N2*L;
πd1 = N2*2L
d1 = 2(d0+Δd)
to find out that each one of them increases it's after-heating-diameter by the same amount as the previous one plus 2*Δd, which corresponds to the increase in volume of a molecule measured radially, thus freeing space for the inner rings and in no way obstructing the expansion.

A rock that is significantly more dense than water is frozen in an ice cube such that the ice cube plus rock is significantly less dense than water. The ice cube is placed in a glass of water, and over time the ice melts. What happens to the water level in the glass? (you do not need to give an exact answer, a rough one will do)
This had been discussed earlier(see page three of this thread). I remember I had an argument with G-Flex about this.

edit: typos, so many typos. I was slightly tipsy when writing this, if this can somwehow absolve me.
« Last Edit: August 28, 2011, 09:16:03 pm by Il Palazzo »
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ed boy

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Re: The questions, riddles and puzzles thread
« Reply #470 on: August 28, 2011, 09:08:25 pm »

A sheet of metal with a circular hole in the middle is heated uniformly. Does the size of the hole increase, decrease, or stay the same?
It increases.
Yup.
A rock that is significantly more dense than water is frozen in an ice cube such that the ice cube plus rock is significantly less dense than water. The ice cube is placed in a glass of water, and over time the ice melts. What happens to the water level in the glass? (you do not need to give an exact answer, a rough one will do)
This had been discussed earlier(see page three of this thread). I remember I had an argument with G-Flex about this.
My bad, I remembered the puzzle without remembering where I got it from.
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Il Palazzo

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Re: The questions, riddles and puzzles thread
« Reply #471 on: August 29, 2011, 08:26:15 am »

How about something like this:
Zdravko the cosmonaut has been manning the space station Mir for 300 days straight. The work he's doing is a healthy mixture of hard and boring. Being a hero of the Stakhanovite movement, he does not complain. What he does complain about, are those pesky aliens who as of late started to make annoying pranks on him. The ground control does not seem to think it's a problem though, and just suggests that he should increase his daily vitamin intake.
One day, Zdravko wakes up floating in space, the bulky body of Mir some 100 meters away and in front of him, fixed motionlessly before his eyes. Judging by the stars in the background, our brave cosmonaut does not appear to be moving in relation to Mir, nor is he rotating.
"Hmm, how did I get here? I don't remember anything from the last few hours" Thinks Zdravko, "An accident while doing EVA? Wait, no! It's those pesky aliens again! Oh how I hate their sense of humour. Oh, well. I guess I should get back to the station."
Zdravko inspects his space suit, and finds out that all he's got on him is a screwdriwer in his suit's pocket. "Lucky me. Let's get to work!"

Questions:
1.How does Zdravko know that it wasn't an accident during work that got him there? He's tired and slightly psychotic, he could've just passed out.
2.How is he going to get back to the warm and safe womb of his space station?(The airlock is still open. All he needs to do is get into hand's reach of the station's body.)
« Last Edit: August 29, 2011, 08:29:06 am by Il Palazzo »
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ed boy

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Re: The questions, riddles and puzzles thread
« Reply #472 on: August 29, 2011, 09:05:20 am »

I don't know how to answer the first question, but I do know how to answer the second.

Simply chuck the screwdriver along the line between him and the space station, but away from the space station. He will therefore start to drift towards the space station, since there are going to be no forces acting upon him, and he will eventually reach it (though it might take a bit of time, as chucking the screwdriver will not give him much momentum).
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Urist Imiknorris

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Re: The questions, riddles and puzzles thread
« Reply #473 on: August 29, 2011, 09:06:39 am »

a) No direct physical link to the station, no broken cable or anything of the sort attached to him. Remember kids - safety first!

b) Throw the screwdriver away from the station.
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Il Palazzo

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Re: The questions, riddles and puzzles thread
« Reply #474 on: August 29, 2011, 09:22:22 am »

Zdravko thinks to himself: "I've heard that the imperialists use cables to connect themselves to their stations when they EVA. Wouldn't that be handy now. I suppose I could make a suggestion to the ground control - they might bring me a spool on the next resupply run."
@Urist I. - Zdrawko never uses cables like that. He probably wouldn't use one even if he had one on the station.

Our cosmonaut analyses his situation. "I could throw a screwdriver away from me to give me some propulsion. That would be terminally stupid though. I'm 100 meters away from the station, maybe more. I would have just one chance at doing it right, and seeing how I'd have to throw it while facing away from the station, I'd be quite sure to misapply the propulsion and drift by without any means to correct my course. Besides, I still have to figure out how to actually turn away from the station that I'm currently facing."
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TheBronzePickle

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Re: The questions, riddles and puzzles thread
« Reply #475 on: August 29, 2011, 09:31:01 am »

The only way he could possibly have had a way to put himself exactly 100 meters away from the station in the same orbit without being attached to it is by having a jetpack that had the sensors necessary to stop him at that perfect distance.
If he has said jetpack, it would be trivially easy to return to the station.
If he's missing the jetpack, obviously something else would have had to put him there, like his alien friends. Whom he should promptly find a way to signal and ask for assistance.
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Il Palazzo

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Re: The questions, riddles and puzzles thread
« Reply #476 on: August 29, 2011, 09:39:21 am »

Yes indeed, there is no way to find oneself floating at a fixed distance from the station like that. To leave the station, one'd have to apply some force that would give him some momentum directed outwards - momentum that would not dissipate, and keep him floating away at a constant velocity. Also, the cosmonaut would be almost equally sure to gain some angular momentum in the process of applying the force, sending him spinning in some wild fashion, unless he took extremally great care to keep the force in line with his centre of mass - rather impossible during an accident.
Well, so he knows it was them aliens. Now let's get him back to the station.
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The Merchant Of Menace

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Re: The questions, riddles and puzzles thread
« Reply #477 on: August 29, 2011, 09:41:09 am »

Well, one assumes he is wearing an oxygen pack, lest he be dead. He could presumably adjust it to allow some air to escape, thereby providing propulsion.

Also, I'm tired, best I could come up with :P
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Max White

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Re: The questions, riddles and puzzles thread
« Reply #478 on: August 29, 2011, 09:44:36 am »

He unscrews himself from what ever he is attached to, drops to the ground, and walks back to Mir?

TheBronzePickle

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Re: The questions, riddles and puzzles thread
« Reply #479 on: August 29, 2011, 09:52:03 am »

There is no ground in space. Unless you're suggesting that he somehow fly down to Earth's surface, walk however many meters it would take to put him directly under Mir, and jump back up into space.
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