MrRubix's Riddle/Problem Thread: Rebirth

[MrRubix]

Alright, so I'm going to start up another one of these again. This thread is not limited to just riddles, but any sort of problems you guys can come up with.


Another riddle:

You have 572 fair quarters and one two-headed quarter (as an aside, hehe, does anyone see the hidden reference thus far?). You pick one quarter at random and flip it 7 times. All heads. What is the probability that you chose the two-headed quarter?

And yet another riddle:

You have two tubs of liquid, where each tub is holding the same volume of liquid. One tub has pure water (Tub 1), and the other has rubbing alcohol (Tub 2). Suppose I pour some amount X from Tub 1 into Tub 2, and then mix well. Then, I pour back amount X from Tub 2 to Tub 1 so that the tubs now possess the same volumes of liquid that they did at the start. What is the relationship between the final concentrations of water in Tub 1 and alcohol in Tub 2?


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Here's an easy problem for mathy types to get you started:

Evaluate (Σ of k=2 to infinity) for (ζ(k)-1)
Where the zeta function (ζ) is defined as:
ζ(s) = (Σ of n=1 to infinity) for 1/(n^s)



And here's a "riddle":

Be as realistic as possible. Answer this question as if you were *actually* in this situation. What would you *actually* do? Don't propose something unless it is something you would *actually* execute.

You're in a building, and there is nobody around to help or hear you. By a very unfortunate turn of events, you find yourself in the middle of a room surrounded by a series of incredibly packed, small, controlled flames. You're holding a pole (say an inch in diameter), which is currently pressed up against a cup (just an ordinary mug, let's say) of gasoline, which is pressed up against the ceiling. The cup is filled up until a sixteenth of an inch below the very top. If *any* gasoline touches any of the flames around you, it will cause a massive chain explosion. The controlled fires will not die out naturally. There is an open window about 12 feet to your left, and there will never be any wind coming in. You are 6 feet tall with average proportions. The ceiling is 15 feet high. The pole is 10 feet long. You may make any other reasonable assumptions. How do you avoid getting killed by this explosion (you can't simply stay there forever... you will eventually faint/pass out/lose strength/etc)?

Here is Gausmaster's attempt at solving the riddle, in realtime: http://www.youtube.com/watch?v=I7tdXQmYXrw

[gausmaster]

Can the cup be balanced on the tip of this pole? If it could be (with some good balancing skill) be done then I would lower it a small amount to alow movement (which could help if balance is lost, the cup could simply be puched back into the ceiling) {then I would move toward a corner and slowly lower the cup agenst the corner (moving the pole slowly away from the corner) untill I could reach it. I would then grab the cup and carefully make my way toward the window. If it was shut & locked I would break it with the pole, and toss the mug out (as far as possible). Then depending on how high the window is I would I would either jump or wait for rescue.

*edit*
acceptable?

[MrRubix]

You could always try it out in real life. Are you really going to risk such movements? Do you trust your balance that much? Can you think of a safer solution?

BTW, walking across the controlled flames would be quite painful.

[gausmaster]

Assuming that the pole is 1 inch in diamiter, yes. Having the safety of the ceiling being so close to the cup almost prevents falls and splashes. The cup would most likely scoot about the ceiling also.

*edit*
Hi19 were you being serious or sarcastic?
I'm dumb, I know.

[hi19hi19]

it's pretty damn easy to balance something an inch in diameter.

[gausmaster]

Oh, I was under the impression the small controled flames were like seperated bundles all over the room. I guess I miss-read b/c you said tightly packed. Still though small flames (assuming I don't catch fire) would be favorable to dieing in an inferno.

I'm guessing you already know a much better answer?

[orlando2k7]

Evaluate (Σ of k=2 to infinity) for (ζ(k)-1)
Where the zeta function (ζ) is defined as:
ζ(s) = (Σ of n=1 to infinity) for 1/(n^s)

the things sum to 1/infinity, which is equal to zero
answer should be -1.

[JurseyRider734]

Lower the pole, grab the mug of gasoline, hold it above your head or w/e so it doesn't get near the flames, get out the window. Or you could just throw the cup out the window and then go out the window yourself.

[gausmaster]

Originally Posted by JurseyRider734

Lower the pole, grab the mug of gasoline, hold it above your head or w/e so it doesn't get near the flames, get out the window. Or you could just throw the cup out the window and then go out the window yourself.

How do you lower a 10 foot pole?



*edit*
lmao Quigly, I'd quote that but I already have you on here.

*edit*
Pntballa, I dont think so. Not without spilling any of the gas.

[Quigly]

Originally Posted by gausmaster

How do you lower a 10 foot pole?

VERY carefully.

[pntballa18]

http://www.youtube.com/watch?v=Mifu3...eature=related

right through the window

[ieatyourlvllol]

Assume an ideal case with the following conditions:

-the centers of the pole and cup have constant coincidence
-the physical interactions are frictionless and bounded only geometrically
-the individual's manipulation of the pole bears impact on only the horizontal position of the cup

The maximum (non-inclusive) allotted vertical distance for (horizontal surface) rotation of the cup on an edge of the pole would be described by (r + 0.5)(sin 45°) where r is the radius of the cup. Thus, the top surface of the cup must be less than (r + 0.5)(sin 45°) from the ceiling. However, as the problem was posed under realistic conditions, I would constrain the upper bound to half (or some reasonable fraction).

With that being established, you would have to lower the stick (and thus cup) to approximately the calculated level and walk extremely slowly while making sure to keep the centers as close as possible. If you were to find the separation too great, you could press the cup up against the ceiling and use friction to readjust, then proceed. Upon finally reaching the window, you would simply kick it out with a foot, and in the few seconds generously provided by gravity...GERONIMO!!!

And if you have the misfortune of being trapped on a particularly high floor...uhh...resort to plan B.

Plan B: Probably the correct solution lol

[JurseyRider734]

Originally Posted by gausmaster

How do you lower a 10 foot pole?



*edit*
lmao Quigly, I'd quote that but I already have you on here.

*edit*
Pntballa, I dont think so. Not without spilling any of the gas.

Well, apparently the ceiling is 15 feet high. Lower it the 5 feet, tilt it a little and catch the cup. A 6' person's arm is probably 2-3 feet so it would only have to fall about a foot until you caught it. You'd have to be pretty careful but I think it's possible.

[gausmaster]

Originally Posted by JurseyRider734

Well, apparently the ceiling is 15 feet high. Lower it the 5 feet, tilt it a little and catch the cup. A 6' person's arm is probably 2-3 feet so it would only have to fall about a foot until you caught it. You'd have to be pretty careful but I think it's possible.

If you could do that without spilling a drop you would deserve to live.

[MrRubix]

You guys should go look at a mug real quick or something. Again, you really don't want to go walking over flames to get to the window. Scooting things along the ceiling is really difficult.

If you're THAT curious, go fill a mug up with water and get something long and skinny to press it against the ceiling. I've actually tried this... it's really, really freaking hard to balance/scoot it, even with frictional readjustment and high riskaversion (that, and your arms tire the hell out). There are better solutions.

[MrRubix]

Originally Posted by orlando2k7

Evaluate (Σ of k=2 to infinity) for (ζ(k)-1)
Where the zeta function (ζ) is defined as:
ζ(s) = (Σ of n=1 to infinity) for 1/(n^s)

the things sum to 1/infinity, which is equal to zero
answer should be -1.

No

[gausmaster]

1. How full is the mug?
2. How did you get a mug on a stick agenst the ceiling in real life?
3. Are the flames taking up all of the floor space excluding your standing area?

[Tasselfoot]

any possibility of the flames sucking the oxygen out of the top of the room... so then it creates a vacuum buildup in the cup so that the cup can suction to the ceiling?

also, all discussions seem to focus on the cup. not on the matter of getting past the fires, which as rubix has said twice now... you can't simply just walk through.


so, assuming the suction could work to suck the cup to the ceiling, possibly swing the pole in front of you, creating bursts of air that would move the fire. might put out a few of the fires such that you could create a path to walk to the window.

[MrRubix]

I edited the first post to explain how full it is. In other words, it's basically full, but not full enough so that you'd be automatically plastering gasoline on the ceiling no matter what.


And, in real life, my roommate stood on a chair and held the cup to the ceiling while I held it up from the bottom, and then he moved away. The pole I used was a sturdy cardboard tube.

BTW, I was able to figure it out in real-time. I had a bunch of paper on the ground to verify that I didn't spill any water.

Tass: Probably not, since there's an open window. Besides, you'd probably die or weaken first from the lack of oxygen even if that happened.

Edited the post to make some other clarifications. The fires are not going to die by themselves, and there is no wind.

[gausmaster]

How much of the room is this fire taking up?