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Everything posted by Rainman

  1. I might be necro-posting here, but I find this interesting. The problem with the "proof" is that it tries to pass off the English language as a formal mathematical language. By what standards do we decide if a sequence of words unambiguously describes a natural number? Are those standards semantic or syntactic? Let's break it down. If certain sequences of words unambiguously describe natural numbers, let S be the set of those sequences. Define the function f : S → N that maps each such sequence of words to the natural number that it describes. Your claim is that f is surjective. Your "pro
  2. I'd hate to disappoint them, but...
  3. I probably shouldn't even be doing math now because I'm quite sick and feverish, but I maintain my stance that we don't have enough information to solve this problem either. We would have to know the probability distribution for French coins among all Euro coins. Imagine for example that French coins would be very rare, with only one Euro coin in a million being French. It is then much more likely that you only have one French coin and simply happened to pull it three times, than that all three coins are French which would be a one in 1018 anomaly. On the other hand, imagine that 90% of all Eu
  4. What part of the body was measured for temperature? Different parts of the body cool at different rates.
  5. Still, I did assume that a+b+c+d = 40. Indeed 12+11+9+8 = 40. My counterexample holds.
  6. What are the allowed operations? Can we only use the standard operations (connect two points or extend a line segment) or may we use other tricks, for example align the straightedge along the diameter and use the other side of the straightedge to draw a parallel line?
  7. 1. Nobody needs to sacrifice himself. The first prisoner to guess has a 50/50 chance of survival, regardless of whether he adheres to the strategy or not. Nothing he can do can improve his chances of survival, so he might as well help the others (not assuming any grudges). 2. Well, yes, the average prisoner most likely is more stupid than the average non-prisoner. But this being a math/logic puzzle, aimed at people who are more intelligent than average, the general assumption is that the prisoners would be intelligent enough to understand the solution proposed by the puzzle solver. And any
  8. How do you arrive at this answer? If I'm not mistaken, the answer is approximated by running the following program indefinitely, given a full list of primes in order P1 = 2, P2 = 3, P3 = 5, and so on: 1: set S = 0, i = 1 2: set S = S + (1-S)/Pi2 3: set i = i+1 4: return to step 2 As this program keeps going, S should tend to the desired probability. Not being a programmer, I haven't been able to run this for large numbers, but it seems to me that it would converge closer to 0.4 than 0.6. I would be very surprised if it converged at exactly 6/pi2, as this would indicate a clear corre
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