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Everything posted by harey

  1. I get the same result as bonanova and Yoruichi-san. Wanting to avoid algebraic errors, I asked Wolfram Alpha: http://www.wolframalpha.com/input/?i=minimize+%28%28x*x%29%2B4%29**%281%2F2%29%2B%28%28x*x%29%2B9%29**%281%2F2%29%2B5-x&lk=4&num=5
  2. What does it mean? I have never been to an orgy
  3. I do not really fancy this kind of problem. The solution usually is "What would answer the god B if the god A asked him what would answer the god C if..." Did you think about something like that?
  4. I am assuming we are looking for the smallest CONSTANT speed. If we want to maximize the travel time (at varying speed), he can travel almost forever: he follows the shadow line moving imperceptibly to the south.
  5. Please post, I think that you cannot get more than 3:
  6. N-1 (except for N=3 or 4 where you can do better). Let's put M=(N-1)/2. If we ask all i to test all i+1, the most unlucky case occurs when all answers are GOOD. Consider that all bad computers are followed by all good ones. We only can be sure the last one is good - there is no bad computer after a good one. If the answer is BAD: - discard both (you never discard two good computers) - substract 1 from i (if i=0, take anyone) - renumber... Now, each computer said the next one is GOOD, so we are in the case (B)(B)(B)..GGGG. In the worst case: a) we always discarded a good computer and a bad one b) both were tested c) there were M bad computers and therefore M discardments d) b+c imply 2*M tests. If a bad computer says BAD, the above still applies. I just hope I did not forget something... @Rainman Suppose: a) BGBXX b) BBGXX c) GGBXX The results of the tests can be GOOD and BAD in each case. 3 and 4 are special cases, so you cannot use them for induction.
  7. We already had this problem, something like drawing two different fruits from a handbag. I just cannot locate it.
  8. If it worked, it would be great for fractal pictures. The bad news is that multiplications are in the processor heavily optimized, a fair guess 4-5 additions. Googling: The big question is how the 3 temporary variables were treated by the compiler. If we have to access the RAM...
  9. @bonanova - sorry, but I believe you have a sign error with the factor bd: I = (a+b)(c+d) - R =ac+bc+ad+bd - (ac - bd) ... = ... +2*bd ....
  10. @bmad As nobody found the solution, can you post it?
  11. Bonus question for those who are at ease with formulae: Using this proceeding, in how many parts can you cut the cake at most?
  12. What does mean "randomly"? If I remember well, there is a controversy how to choose randomly points on a circle.
  13. There is: just the formula giving the number of boys. But it is quite unreadable and to understand it, you have more or less to go thru what I have written.
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