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About plasmid

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  1. Host - maurice Red - Blue - dee Green - Araver Purple - Plainglazed Orange - marksmanjay LimeGreen - LoGo Cyan - plasmid Brown - HotPink - nana Gray - Framm I'll be NCyan Cat.
  2. I'm not sure how to even approach this analytically. But I was able to get some C code working very efficiently, and found that every number up to at least a billion can be represented by the sum of a triangular, square, and pentagonal number. This algorithm starts of with the pentagonal number as large as it can be without exceeding the target value and gradually decreases the pentagonal number if there are no combination of a triangle and square with it that can hit the target value, so finding a solution with a large pentagonal number is suggestive that there are many solutions for that target value. And when you get in the range of these large numbers, the pentagonal number is much greater than the triangular or square number. Output for some of the larger numbers (The algorithm only prints out solutions at every 1,000,000 values so it doesn't lose efficiency simply from printing out all the results, but it calculates a solution for every value, and would stop if it hits a value with no solution.) C code
  3. I believe this gets honors as the best "cheating" answer thus far.
  4. These partial differential equations are beyond me at the moment. But for the follow-on question, I'll posit the following:
  5. Addendum to this answer:
  6. That phrase was posted on Brainden?!? Regarding pumping, I'm not sure how that would work out in practice. If the starting situation has the acrobat on a platform with the trapeze rope essentially going horizontally, then if you add more force to the swing you'll end up going above horizontal on the other side before gravity pulls you back down, and you wouldn't be swinging like a pendulum but more like a weight on a rope that was just held out somewhere in space and dropped. So you could pump exactly once before letting go. And motorizing the pivot points of the trapezi is certainly enough of a cheat to qualify as a Puzzle Land answer.
  7. Correct, initial velocity is zero. The answer is independent of whatever value you choose for gravitational force, but you could use 9.8 m/s2 if you like.
  8. An acrobat can release the trapeze at any point and follow the usual laws of physics (of a point mass without wings or rocket engines or such) until coming into contact with the other trapeze bar. Will add a drawing next if that would help.
  9. The non-cheating solution I have doesn't involve the sorts of things you speak of. The acrobats can be considered as points that can attach to and release from a trapeze at a distance rope length from the trapeze's axis, and that just follow Newtonian mechanics aside from being able to grab onto the trapezi (or whatever the plural of trapeze is).
  10. I came up with a solution where the distance between the platforms could be greater than height * 4, even with a level floor. Having the platforms as far apart as you want and making the acrobats hoof it across the circus grounds counts as a legitimate cheating (and thus paradoxical) answer, and is so far the best for others to try to top.
  11. Right on, Wilson
  12. Not a hockey goalie, fisherman, or cartographer. I like how goalie fits with these clues very well even though the clues aren't interpreted in the way I had in mind. But the second stanza is difficult to fit with that answer. I like the reasoning behind the fisherman answer as well, but once the answer is revealed there will be a much clearer interpretation of the clue about Atlas and the last line's use of the word dearth implies that two would be an unacceptably low number (and for the sake of hinting, the dearth in the last line refers to Atlas' feet from the previous line). A cartographer is actually closer to my answer than you might think.
  13. Indeed not an asteroid impact. I'm thinking that once the answer is seen, all of the clues will become visible and make sense. (There might be hinting in here.)