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