Solutions to Ken's LED Puzzle

kenled

digits = [

#          B C                  D           A B C             A B C   
#        E     F                F                 F                 F 
#        G     H                H                 H                 H 
#        I     L                L             J K               J K   
#        M     N                N           M                       N 
#        O     P                P           O                       P 
#          R S                  T           Q R S T           Q R S   
#               
    "BCEFGHILMNOPRS",      "DFHLNPT",   "ABCFHJKMOQRST",   "ABCFHJKNPQRS",
#                                                                  
#                  
#        A                A B C D             B C             A B C D 
#        E     F          E                 E                       F 
#        G     H          G                 G                       H 
#        I J K L          I J K             I J K                   L 
#              N                N           M     N                 N 
#              P                P           O     P                 P 
#              T          Q R S               R S                   T 

     "AEFHIJKLNPT",  "ABCDEGIJKNPQRS",   "BCEGIJKMNOPRS",    "ABCDFHLNPT",
                 
#                  
#          B C              B C               B C             A B C   
#        E     F          E     F           E     F           E     F 
#        G     H          G     H           G     H           G     H 
#          J K              J K L           I J K L           I J K   
#        M     N                N           M     N           M     N 
#        O     P                P           O     P           O     P 
#          R S              R S             Q     T           Q R S   
#
   "BCEFGHJKMNOPRS", "BCEFGHJKLNPRS", "BCEFGHIJKLMNOPQT", "ABCEFGHIJKMNOPQRS",                 
#                    
#          B C D          A B C             A B C D           A B C D 
#        E                E     F           E                 E       
#        G                G     H           G                 G       
#        I                I     L           I J K             I J K   
#        M                M     N           M                 M       
#        O                O     P           O                 O       
#          R S T          Q R S             Q R S T           Q       
#
     "BCDEGIMORST", "ABCEFGHILMNOPQRS",  "ABCDEGIJKMOQRST", "ABCDEGIJKMOQ" ]

          
from itertools import combinations, product

for n in [6,5,4]:
  count = 0
  for combo in combinations("ABCDEFGHIJKLMNOPQRST", n):
    buckets = [None]*(2**n)
    for digit in digits:
      sig = reduce(lambda a, b: (a<<1) + int(b), [c in digit for c in combo])
      if buckets[sig] is not None: break
      buckets[sig] = digit

    else:  # (didn't break)
      print "".join(combo)
      count += 1

  print "\n%4d solutions for n = %d\n" % (count,n)

print; print "~fini~"