3 ms·

I'd be very interested if you could explain it properly without using math, natural logarithms and Euler's constant as the linked solution does.

• RiderOfGiraffes 16y ago
  Your arguing a different question. Getting the exact answer isn't the same as making it understandable. You don't need the math to get a feel for what's happening.
  • srgseg 16y ago
    To be fair, when the puzzle specifically asks: What are the best odds the prisoners can give themselves? (Hint: it's better than 1/2^100.) that is clearly an impossible ask without advanced mathematics, and anyone without such advanced math knowledge will not be therefore able to solve the problem.
    • RiderOfGiraffes 16y ago
      I think we're arguing from different premises. I think that once you know the algorithm, getting an answer of "around 30% to 35%" is both easily within the grasp of a reasonably educated person, and within the spirit of the statement. The problem is getting the algorithm at all. The idea of chasing cycles is pretty common to mathematicians, and should be well-known to computer scientists, but is not well-known otherwise. To that extent, finding the algorithm will come more naturally to people who are familiar with discreet math. If you want an answer that's exactly right in the limit then you certainly need more math, and quite a lot of it, but simple counting arguments get you between 20% and 40%. A little more care gets you "around 30%." Perhaps you think that's "advanced math." I don't, and have done it in math enrichment classes for 14 year-olds. It's not in their curriculum, but the curriculum is so impoverished that's no surprise to anyone. <shrug> Not much point in debating it further.