49 lines
968 B
Python
49 lines
968 B
Python
#!/usr/bin/env python3
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from math import gcd
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from itertools import combinations_with_replacement as combs
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from math import sqrt
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def points(a, b, c, d):
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return (gcds[a][b] + gcds[b][c] + gcds[c][d] + gcds[d][a])//2 + 1
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def is_square(n):
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return sieve[n]
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def refs(a,b,c,d):
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r = [ (a,b,c,d),
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(d,a,b,c),
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(c,d,a,b),
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(b,c,d,a),
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(a,d,c,b),
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(b,a,d,c),
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(c,b,a,d),
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(d,c,b,a)]
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return list(set(r))
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count = 0
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m = 100
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space = range(1, m+1)
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gcds = [None for n in range(m+1)]
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for a in range(1, m+1):
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gcds[a] = [0] + [a*b - gcd(a,b) for b in range(1, m+1)]
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sieve = [False] * 2*m**2
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n = 1
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while n**2 < len(sieve):
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sieve[n**2] = True
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n += 1
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for a,b,c,d in combs(space, 4):
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perms = [(a,b,c,d), (a,c,b,d), (a,c,d,b)]
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wins = set()
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for p in perms:
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if not is_square(points(*p)):
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continue
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wins |= set(refs(*p))
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count += len(wins)
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print(count)
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