Answer To The Star Problem

A reddit user posted a link to a puzzle with the title "Can You Solve This Problem". Not one to refuse a challenge, I took it up.

20 minutes later, I found a whole bunch of solutions. The code follows:

#Problem: arrange the numbers range(1, 13) on a six-point #star so that every line adds up to 26. ASCII: # 1 2 # 3 # 4 5 # 6 7 # 8 9 # 10 # 11 12 # # the vertices are 1,2,6,7,11,12. The 6 lines are #(1,3,5,7), (1,4,8,11), #(2,3,4,6), (2,5,9,12), #(7,9,10,11), #(12,10,8,6), # # So, given the first twelve integers ints = range(1, 13) # # we can test if we have a satisfied solution: def solved(perm): #lines are the same as above, but with one subtracted from each number to #make them into array indices lines = [(0,2,4,6), (0,3,7,10), (1,2,3,5), (1,4,8,11), (6,8,9,10), (11,9,7,5)] for line in lines: if sum(perm[i] for i in line) != 26: return False return True #and, as a gut check, let's figure out a way to print it def pretty_print_star(permutation): print """ %s %s %s %s %s %s %s %s %s %s %s %s """ % tuple(permutation) # now! the brute force way to search for solutions would be to try and permute # a list of all 12 integers, and wait for "solved" to be true. I'll import a # permute function: # (requires probstat: http://probstat.sourceforge.net/ ) import probstat for perm in probstat.Permutation(ints): if solved(perm): print "found solution!" pretty_print_star(perm)