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ModelOfTheory's profile
Model Of Theory
Model Of Theory
Model Of Theory
@ModelOfTheory

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Model Of Theory

@ModelOfTheory

ZFC, THIS.

Joined July 2016

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    1. Shredder Rawflesh‏ @RadishHarmers 16 May 2017

      An empirical observation about this kids' problem going around, which math folk can try to beat me to explaining: https://www.nytimes.com/2017/05/15/us/math-counts-national-competition.html …

      2 replies 0 retweets 0 likes
    2. Shredder Rawflesh‏ @RadishHarmers 16 May 2017
      Replying to @RadishHarmers

      With 4N chickens, the number of unpecked chickens is symmetrically distributed (probability of x matches probability of 2N - x).

      1 reply 0 retweets 0 likes
    3. Shredder Rawflesh‏ @RadishHarmers 16 May 2017
      Replying to @RadishHarmers

      Not true if num chickens not divisible by 4. Anyway, I don't yet know why this is the case; I've just observed it empirically for lower N.

      1 reply 0 retweets 0 likes
    4. Shredder Rawflesh‏ @RadishHarmers 16 May 2017
      Replying to @RadishHarmers

      Well, I just drank fluids and slept all day and didn't crack it. But I'm disheartened to see no one else did either.

      3 replies 0 retweets 0 likes
    5. Model Of Theory‏ @ModelOfTheory 16 May 2017
      Replying to @RadishHarmers

      Relevant involution: Chicken switches direction of peck if it is 0 or 1 mod 4.

      1 reply 0 retweets 1 like
    6. Shredder Rawflesh‏ @RadishHarmers 16 May 2017
      Replying to @ModelOfTheory

      I kept thinking about this involution, but it's not obvious to me why it works.

      1 reply 0 retweets 0 likes
      Model Of Theory‏ @ModelOfTheory 16 May 2017
      Replying to @RadishHarmers

      For each chick, 1 of nhbrs switches, so single-pecked chicks and non-or-double-pecked chicks swapped. Same # of non-pecked, double-pecked.

      4:58 PM - 16 May 2017
      • 1 Like
      • Shredder Rawflesh
      1 reply 0 retweets 1 like
        1. New conversation
        2. Shredder Rawflesh‏ @RadishHarmers 16 May 2017
          Replying to @ModelOfTheory

          Ah, beautiful. All props to you.

          1 reply 0 retweets 0 likes
        3. Shredder Rawflesh‏ @RadishHarmers 16 May 2017
          Replying to @RadishHarmers @ModelOfTheory

          Other observations I made, for what it's worth: With even chickens, swapping every alternate chickens' directions keeps peck # unchanged.

          1 reply 0 retweets 0 likes
        4. Shredder Rawflesh‏ @RadishHarmers 16 May 2017
          Replying to @RadishHarmers @ModelOfTheory

          And the total number of unpecked is equal to the total number of contiguous blocks of chickens facing same direction, of size > 1 and < all.

          1 reply 0 retweets 0 likes
        5. Shredder Rawflesh‏ @RadishHarmers 16 May 2017
          Replying to @RadishHarmers @ModelOfTheory

          So close to seeing it, and yet fell just short. Oh well. Math.

          1 reply 0 retweets 0 likes
        6. Shredder Rawflesh‏ @RadishHarmers 22 May 2017
          Replying to @RadishHarmers

          With n total chickens, the probability of x unpecked chickens is ((n choose 2x) + g(n, x) * (n/2 choose x)) * 2^(1 - n), where g(n, x) is…

          1 reply 0 retweets 0 likes
        7. Shredder Rawflesh‏ @RadishHarmers 22 May 2017
          Replying to @RadishHarmers

          0 if n is odd -1 if n is even and x is odd 1 if n is even and x is even (x assumed integer; whole probability should be taken 0 otherwise.)

          0 replies 0 retweets 0 likes
        8. End of conversation

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