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    Where, in the Universe, are we?

    Although it's honestly not something I know much about, it might be of interest to you to know that there is a doppler shift in the cosmic background radiation. I don't believe this tells us anything about position, but it might indicate motion or something else like proximity to a black hole. I...
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    Circular Polarization and the Search for Semi-Intelligent Life

    It took me a little while to wrap my head around circularly polarized light, or more specifically how this can be done "passively". Wikipedia didn't do much help until I found the article at Polarizer, if any of you were wondering how the new 3D movie technology works. My first question is...
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    Where do neutrinos go?

    Neutrinos have mass... insignificant mass, we are told, as their speed is so near that of light we can't even observe the difference. On the other hand, there are a lot of them. Every year the Sun produces something like half a tredecillion neutrinos, if my math is right. Depending on the mass...
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    Dark matter/energy

    I said what's called "dark energy" should probably just be called "dark mystery". I never said dark matter wasn't matter. And you're accusing ME of strawman? I don't know what that means. To me energy is the capacity to do work. Does gravity have energy? I wouldn't have thought so, and if...
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    Dark matter/energy

    Oh, thank God! For the past day or two I thought for certain we were all doomed. Thank you for your reply. I think I'd rather be hurled out into intergalactic space than pulled into the event horizon. On the other hand, watch what you wish for, right? Couldn't this be explained more simply...
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    Dark matter/energy

    Frankly I agree with you. This dark matter/dark energy nonsense fits the universe to our flawed explanation of how it works, assuming the laws and making preposterous conclusions, rather than finding a simple explanation for how the universe actually does work. The mistake we are making is...
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    How Common is the Incompleteness Phenomenon?

    Wow, I think you just proved that math is evil. Okay then, there must be a hole in my sketchy "proof" somewhere. I've tried to reformulate it more formally and I'm hitting a stumbling block in that, whereas I used a proof by contradiction above, I can't assume that a characterization of...
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    How Common is the Incompleteness Phenomenon?

    Yes, "neither provable nor disprovable" is equivalent to "independent of the axioms". It was my understanding that, at least in some cases, it's possible to prove that A is in that categorty, that the axioms plus A are consistent if and only if the axioms plus not A are consistent, which...
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    How Common is the Incompleteness Phenomenon?

    I understand the connecion between "constructions of mathematical systems" and computability by Turing machines, or at least I did back in the day, but the connection between that and Gödel's Incompleteness Theorem isn't so clear or immediate. Incompleteness is indeed a strange thing, maybe...
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    Math Problem

    The sum of three children's ages is x. The product of their ages is y more than the product of their ages this time last year. What is the sum of the squares of the children's ages? x*x + 2(1-x-y)
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    Executioner riddle

    Moreover than that, we don't know that they speek English. For a negatively stated question such as "Aren't you a god?" some languages would have you answer differently; in French, in fact, there is a different "yes" answer to such a question. In Mandarin, a yes/no question will be answered with...
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    Searching for a non-negative integer

    Sorry, I don't remember how to solve Diophantine equations off the top of my head. Anyways, where's the brain teaser?
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    Brain Teaser #94

    The formula is correct. I can't believe that, in coming up with the problem, I subtracted one from the factors of 2^blah instead of adding one. You may have found two solutions instead of the lone one I had expected, but thankfully it turns out there is some solution after all.
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    Triangle Puzzle

    I said "something like that" because I was writing from memory. Anyways I labeled a different angle as x. If that's true then I'm convinced there is a right angle in the figure, resulting in even more symmetry. Working backwards from my presumption there are at least seven formulas that, if...
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    Brain Teaser #94

    There should be a pattern. The more interesting is the constructive proof of the formula. That's it.
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    Triangle Puzzle

    This problem is evil. Please tell me that the answer is at least a multiple of 10 degrees. Using sine law and some of the symmetry in the figure, I got it down to (sin x)/(sin x+20) = (sin 80)/(sin 40) or something like that, but I don't know how to solve such a complex equation without using...
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    Simple code

    Translate it to Chinese and assign each Chinese character to a LISP function. Compile and run the program and encode the output by using it as a seed to a random number generator. Then subtract one.
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    Brain Teaser #94

    I don't think anyone's going to crank this one out by brute force.
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    Brain Teaser #98

    Gokul with the point!
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    Brain Teaser #98

    I heard this one a while back: A Hungarian community of married mathematicians has the following tradition: should any man determine that his wife cheated on him, he shall hang himself at noon. The townsfolk being rather introverted, there is little gossip except when there is an affair. In...
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    Brain Teaser #94

    Nice formula. How did you come across it? True. You could also make that into a stronger statement fairly easily.
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    Brain Teaser #94

    gnome with the point! I thought people would get frustrated with this one because there aren't any solutions where the two lengths are integers. It just goes to show that you can't fool everyone. For the theoretical types, here is another problem. I should warn you that there is only one...
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    Brain Teaser #93

    Except that it's the toddler version, for creators with brain spasms. Next time I'll let Njorl come up with the chess problems.
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    Brain Teaser #93

    Wow, that was a fast response! But no, I meant attack or defend. This is analogous to the eight queens problem.
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    Brain Teaser #94

    Brain Thumper #8 The Pacific Proprietary Production Plant has the capacity to manufacture straight sections of miniature railroad track on two machines, each of which produces a specific length of track. For instance, suppose that the company had initially configured the machines to make...
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    Brain Teaser #84

    What I mean is, find the significance of the first sequence. To that end, I have provided a formula that will prove useful, without giving too much away.
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    Brain Teaser #93

    Brain Thumper #7 What is the greatest number of knights that can be placed on a chessboard such that no two pieces are in a position to attack each other? Please provide your solution.
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    Brain Teaser #84

    As noted, there are primes missing, so they do not yield all of the prime powers of 2.
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    Brain Teaser #91

    I'm not sure how you're counting ten. The five perimeter routes are crosstown since the downtown area is the center of the city. The express buses are a variation of the regular buses. It's really the same numbered route, just a different type of service. By "route" I meant a bus route...
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    Brain Teaser #91

    Yes! Using a different method I also got an average break of 8:20. Using your method for the case of 60 operators I came up with 95/11 or a little closer to 9 minutes, so I think you may have made an arithmetic mistake earlier. No, I originally wanted the average headway to be 10-15...
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