64 lines
1.2 KiB
Python
64 lines
1.2 KiB
Python
def choose(xs, n):
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"""
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Computes r choose n, in other words choose n from xs.
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Returns combinations and not permutations.
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"""
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if not xs or n == 0:
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return [[]]
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if len(xs) == n:
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return [xs]
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rs = []
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x = xs[0]
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for r in choose(xs[1:], n - 1):
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rs.append([x] + r)
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for r in choose(xs[1:], n):
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rs.append(r)
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return rs
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def pairs(xs):
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if len(xs) == 2:
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return [xs]
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r = []
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a = xs[0]
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for b in xs[1:]:
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r.append([a, b])
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return r + pairs(xs[1:])
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def can_form_squares(pair):
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xs, ys = pair
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# replace 9s with 6s
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for d, e in [(0, 1), (0, 4), (0, 6), (1, 6),
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(2, 5), (3, 6), (4, 6), (6, 4), (8, 1)]:
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if d in xs and e in ys:
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continue
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elif e in xs and d in ys:
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continue
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return False
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return True
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def euler_090():
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# replace 9s with 6s to handle "up-side down usage of 6" without hassle
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xs = list(range(0, 9)) + [6]
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cs = choose(xs, 6)
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ps = pairs(cs)
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count = 0
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for p in ps:
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if can_form_squares(p):
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count += 1
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return count
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if __name__ == "__main__":
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solution = euler_090()
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print("e090.py: " + str(solution))
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assert(solution == 1217)
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