project-euler-python.py/problem68_py.txt at master · bashareid/project-euler-python.py · GitHub

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"""
You can solve it using recursion , the idea is to forget the problem where should you begin in the question you should begin with the set that has
the smallest number i generated all possible combinations then with a little bit of thinking you will notice that the number must begin with 6 and
the inner loop must containe 1, 2, 3, 4, 5 then you will find it easy.

"""
lower_bound = 1
upper_bound = 11
combinations = []
total = []

for a in range(lower_bound, upper_bound):
  for b in range(lower_bound, upper_bound):
    if a != b:
      for c in range(lower_bound, upper_bound):
        if a != c and b != c:
          for d in range(lower_bound, upper_bound):
            if a != d and b != d and c != d:
              for e in range(lower_bound, upper_bound):
                if a != e and b != e and c != e and d != e:
                  for f in range(lower_bound, upper_bound):
                    if a != f and b != f and c != f and d != f and e != f:
                      for g in range(lower_bound, upper_bound):
                        if a != g and b != g and c != g and d != g and e != g and f != g:
                          for h in range(lower_bound, upper_bound):
                            if a != h and b != h and c != h and d != h and e != h and f != h and g != h:
                              for i in range(lower_bound, upper_bound):
                                if a != i and b != i and c != i and d != i and e != i and  f != i and g != i and h != i:
                                  for j in range(lower_bound, upper_bound):
                                    if a != j and b != j and c != j and d != j and e != j and  f != j and g != j and h != j and i != j:
                                      x = [a, b, c]
                                      y = [d, c, e]
                                      z = [f, e, g]
                                      m = [h, g, i]
                                      n = [j, i, b]
                                      if sum(x) == sum(y) == sum(z) == sum(m) == sum(n):
                                        combinations.append((int(str(a) + str(b) + str(c) + str(d) + str(c) + str(e) + str(f) + str(e) + str(g)
                                          + str(h) + str(g) + str(i) + str(j) + str(i) + str(b)), sum([c, e, g, i, b])))

combinations = sorted(combinations, key = lambda s: s[1], reverse=False)
minimum = combinations[0][1]
highest = 0
for i in combinations:
  if len(str(i[0])) == 16 and str(i[0])[0] == '6':
    if highest < i[0] and i[1] == minimum:
      highest = i[0]
print(highest)