#Note: in addition to the "official" solutions, I'm giving other, in some #ways nicer, solutions. Studying them would be nice, but optional. def is_symmetric(L): return L == L[::-1] def is_symmetric_loop(L): for i in range(len(L)//2): if L[i] != L[-i-1]: return False return True ################################################################################ #Official solution def is_near_symmetric2(L): for i in range(len(L)): for j in range(i + 1, len(L)): L[i], L[j] = L[j], L[i] sym = is_symmetric(L) L[i], L[j] = L[j], L[i] if sym: return True return False #A more efficient (but more difficult) version of is_near_symmetric, #(thanks to Ben) def is_near_symmetric(L): if is_symmetric(L): return True for i in range(len(L)//2): if L[i] != L[-i-1]: break remember_i = i for i in range(remember_i+1, len(L)//2): if L[i] != L[-i-1]: if L[i] == L[remember_i]: L[-i-1], L[remember_i] = L[remember_i], L[-i-1] elif L[-i-1] == L[remember_i]: L[i], L[remember_i] = L[remember_i], L[i] else: L[i], L[len(L)//2] = L[len(L)//2], L[i] return is_symmetric(L) return False #A quick program to verify that both functions return the same thing for i in range(3): for j in range(3): for k in range(3): for l in range(3): for m in range(3): for n in range(3): L = [i, j, k, l, m, n] if s2(L[:]) != is_near_symmetric(L[:]): print(L, is_near_symmetric2(L[:]), is_near_symmetric(L[:])) L = [i, j, k, l, m] if s2(L[:]) != is_near_symmetric(L[:]): print(L, is_near_symmetric2(L[:]), is_near_symmetric(L[:])) ################################################################################ #Official solution def sum8_0(L): for i0 in [0, 1]: for i1 in [0, 1]: for i2 in [0, 1]: for i3 in [0, 1]: for i4 in [0, 1]: for i5 in [0, 1]: for i6 in [0, 1]: for i7 in [0, 1]: if i0 + i1 + i2 + i3 + i4 + i5 + \ i6 + i7 == 0: continue s = i0*L[0] + i1*L[1] + i2*L[2] + \ i3*L[3] + i4*L[4] + i5*L[5] + \ i6*L[6] + i7*L[7] if s == 0: return True return False sum8_0([10, 1, 2, 3, 4, 5, -6, 7]) #A nicer, but more difficult, version (thanks to Susanna) def sumn_0(L): sums = [0] #sums[1:] is all the sums for e in L: new_sums = [] for s in sums: new_sums.append(s + e) sums.extend(new_sums) return 0 in sums[1:] sumn_0([4, 1, 1, 2, 10, -12]) #A recursive solution, to be covered in a few weeks: def is_subset_sum(L, target = 0): if len(L) == 0: return False if L[0] == target: return True return is_subset_sum(L[1:], target) or is_subset_sum(L[1:], target-L[0]) #How about the version that will give you carpal tunnel synrdome? Let's generate #it! (Without using advanced tools...) program = "def auto_sum_0(L):\n" for i in range(n): for i0 in [0, 1]: for i1 in [0, 1]: for i2 in [0, 1]: for i3 in [0, 1]: for i4 in [0, 1]: for i5 in [0, 1]: for i6 in [0, 1]: for i7 in [0, 1]: elem_on = [i0, i1, i2, i3, i4, i5, i6, i7] if sum(elem_on) == 0: continue sum_str = "" for i in range(8): if elem_on[i] == 1: sum_str += "L[%d] + " % (i) sum_str += "0" program += " if %s == 0:\n return True\n" % (sum_str) program += " return False" exec(program) auto_sum_0([4, 1, 1, 2, 10, 50, 7, 8]) print(program) ##Output: # In [110]: print(program) # def auto_sum_0(L): # if L[7] + 0 == 0: # return True # if L[6] + 0 == 0: # return True # if L[6] + L[7] + 0 == 0: # return True # if L[5] + 0 == 0: # return True # if L[5] + L[7] + 0 == 0: # return True # if L[5] + L[6] + 0 == 0: # return True # if L[5] + L[6] + L[7] + 0 == 0: # return True # if L[4] + 0 == 0: # return True # if L[4] + L[7] + 0 == 0: # return True # if L[4] + L[6] + 0 == 0: # return True # if L[4] + L[6] + L[7] + 0 == 0: # return True # if L[4] + L[5] + 0 == 0: # return True # if L[4] + L[5] + L[7] + 0 == 0: # return True # if L[4] + L[5] + L[6] + 0 == 0: # return True # if L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[3] + 0 == 0: # return True # if L[3] + L[7] + 0 == 0: # return True # if L[3] + L[6] + 0 == 0: # return True # if L[3] + L[6] + L[7] + 0 == 0: # return True # if L[3] + L[5] + 0 == 0: # return True # if L[3] + L[5] + L[7] + 0 == 0: # return True # if L[3] + L[5] + L[6] + 0 == 0: # return True # if L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[3] + L[4] + 0 == 0: # return True # if L[3] + L[4] + L[7] + 0 == 0: # return True # if L[3] + L[4] + L[6] + 0 == 0: # return True # if L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[3] + L[4] + L[5] + 0 == 0: # return True # if L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[2] + 0 == 0: # return True # if L[2] + L[7] + 0 == 0: # return True # if L[2] + L[6] + 0 == 0: # return True # if L[2] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[5] + 0 == 0: # return True # if L[2] + L[5] + L[7] + 0 == 0: # return True # if L[2] + L[5] + L[6] + 0 == 0: # return True # if L[2] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[4] + 0 == 0: # return True # if L[2] + L[4] + L[7] + 0 == 0: # return True # if L[2] + L[4] + L[6] + 0 == 0: # return True # if L[2] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[4] + L[5] + 0 == 0: # return True # if L[2] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[2] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[2] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[3] + 0 == 0: # return True # if L[2] + L[3] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[6] + 0 == 0: # return True # if L[2] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[5] + 0 == 0: # return True # if L[2] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[2] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[4] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + 0 == 0: # return True # if L[1] + L[7] + 0 == 0: # return True # if L[1] + L[6] + 0 == 0: # return True # if L[1] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[5] + 0 == 0: # return True # if L[1] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[4] + 0 == 0: # return True # if L[1] + L[4] + L[7] + 0 == 0: # return True # if L[1] + L[4] + L[6] + 0 == 0: # return True # if L[1] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[4] + L[5] + 0 == 0: # return True # if L[1] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[3] + 0 == 0: # return True # if L[1] + L[3] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[6] + 0 == 0: # return True # if L[1] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[5] + 0 == 0: # return True # if L[1] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[4] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + 0 == 0: # return True # if L[1] + L[2] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[5] + 0 == 0: # return True # if L[1] + L[2] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[4] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[5] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[5] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + 0 == 0: # return True # if L[0] + L[7] + 0 == 0: # return True # if L[0] + L[6] + 0 == 0: # return True # if L[0] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[5] + 0 == 0: # return True # if L[0] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[4] + 0 == 0: # return True # if L[0] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[3] + 0 == 0: # return True # if L[0] + L[3] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[6] + 0 == 0: # return True # if L[0] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[5] + 0 == 0: # return True # if L[0] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[4] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + 0 == 0: # return True # if L[0] + L[2] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[5] + 0 == 0: # return True # if L[0] + L[2] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[4] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[5] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + 0 == 0: # return True # if L[0] + L[1] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[4] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[7] + 0 == 0: # return True # if L[6] + 0 == 0: # return True # if L[6] + L[7] + 0 == 0: # return True # if L[5] + 0 == 0: # return True # if L[5] + L[7] + 0 == 0: # return True # if L[5] + L[6] + 0 == 0: # return True # if L[5] + L[6] + L[7] + 0 == 0: # return True # if L[4] + 0 == 0: # return True # if L[4] + L[7] + 0 == 0: # return True # if L[4] + L[6] + 0 == 0: # return True # if L[4] + L[6] + L[7] + 0 == 0: # return True # if L[4] + L[5] + 0 == 0: # return True # if L[4] + L[5] + L[7] + 0 == 0: # return True # if L[4] + L[5] + L[6] + 0 == 0: # return True # if L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[3] + 0 == 0: # return True # if L[3] + L[7] + 0 == 0: # return True # if L[3] + L[6] + 0 == 0: # return True # if L[3] + L[6] + L[7] + 0 == 0: # return True # if L[3] + L[5] + 0 == 0: # return True # if L[3] + L[5] + L[7] + 0 == 0: # return True # if L[3] + L[5] + L[6] + 0 == 0: # return True # if L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[3] + L[4] + 0 == 0: # return True # if L[3] + L[4] + L[7] + 0 == 0: # return True # if L[3] + L[4] + L[6] + 0 == 0: # return True # if L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[3] + L[4] + L[5] + 0 == 0: # return True # if L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[2] + 0 == 0: # return True # if L[2] + L[7] + 0 == 0: # return True # if L[2] + L[6] + 0 == 0: # return True # if L[2] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[5] + 0 == 0: # return True # if L[2] + L[5] + L[7] + 0 == 0: # return True # if L[2] + L[5] + L[6] + 0 == 0: # return True # if L[2] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[4] + 0 == 0: # return True # if L[2] + L[4] + L[7] + 0 == 0: # return True # if L[2] + L[4] + L[6] + 0 == 0: # return True # if L[2] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[4] + L[5] + 0 == 0: # return True # if L[2] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[2] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[2] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[3] + 0 == 0: # return True # if L[2] + L[3] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[6] + 0 == 0: # return True # if L[2] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[5] + 0 == 0: # return True # if L[2] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[2] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[4] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[2] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + 0 == 0: # return True # if L[1] + L[7] + 0 == 0: # return True # if L[1] + L[6] + 0 == 0: # return True # if L[1] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[5] + 0 == 0: # return True # if L[1] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[4] + 0 == 0: # return True # if L[1] + L[4] + L[7] + 0 == 0: # return True # if L[1] + L[4] + L[6] + 0 == 0: # return True # if L[1] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[4] + L[5] + 0 == 0: # return True # if L[1] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[3] + 0 == 0: # return True # if L[1] + L[3] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[6] + 0 == 0: # return True # if L[1] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[5] + 0 == 0: # return True # if L[1] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[4] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + 0 == 0: # return True # if L[1] + L[2] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[5] + 0 == 0: # return True # if L[1] + L[2] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[4] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[5] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[5] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[1] + L[2] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + 0 == 0: # return True # if L[0] + L[7] + 0 == 0: # return True # if L[0] + L[6] + 0 == 0: # return True # if L[0] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[5] + 0 == 0: # return True # if L[0] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[4] + 0 == 0: # return True # if L[0] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[3] + 0 == 0: # return True # if L[0] + L[3] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[6] + 0 == 0: # return True # if L[0] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[5] + 0 == 0: # return True # if L[0] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[4] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + 0 == 0: # return True # if L[0] + L[2] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[5] + 0 == 0: # return True # if L[0] + L[2] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[4] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[5] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[2] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + 0 == 0: # return True # if L[0] + L[1] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[4] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[5] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[6] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[5] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[5] + L[7] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[5] + L[6] + 0 == 0: # return True # if L[0] + L[1] + L[2] + L[3] + L[4] + L[5] + L[6] + L[7] + 0 == 0: # return True # return False