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Everything posted by EventHorizon

  1. Beat me to it, kudos CaptainEd. I guessed the solution and came up with a proof while trying to get to sleep last night. The first step was inelegant, so I was going to work on it a bit before posting. This problem reminded me a lot of
  2. I'd say that the minimum value of f is slightly less than... I'll play around with it a bit to see how much I can lower it. Another interesting addition might be, once the minimum f is found, to find the minimum travel distance (e.g., amount of gas) needed for some f a little higher than the minimum.
  3. addendum: I didn't come up with this myself. Monty Hall was asked about the Monty Hall problem, and his response was such.
  4. n factorial (represented as n!) is the product of all positive integers up to n. So the number you are looking for is 1,000,000! ("one million factorial")
  5. I'm sure I know what BMAD was saying. Yes, ignore the units / squared units difference. The problem doesn't involve a circle though. You need to find a function f(x) such that the area under the curve between two points is the same as the arc length between those two points along the function. Here the arc length is like the length of a string representing the function cut at the two points. How to find the arc length of a function: Restatement of problem using previous spoiler: One answer is simple, the other is less so.
  6. I looked at that for a while. Though it's not much, here's what I got...
  7. This puzzle is not quite solved yet. So here's my attempt
  8. I installed the plus4 app, and it is just a mastermind clone. +x means you have x numbers in the right spot, and -x means you have x numbers right, but they are in the wrong spots. It could be that a guess would result in +2-2, meaning that you have all the right numbers, but two are in the wrong spots.
  9. So the best you can do is 00 00 or 0 0 ... 0 0 000...00
  10. Looks like I misunderstood the initial configuration. I assumed the x's were already amoeba and not just space to vacate.
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