test.py

lights = [['g','r'],
          ['y','d'],
          ['r','r'],
          ['b','d'],
          ['g','r'],
          ['b','r'],
          ['y','d'],
          ['p','d'],
          ['b','d'],
          ['r','d'],
          ['b','r']]

def encoder(items, key, reverse=False):
  green, yellow, red, blue, purple, right, down = key
  translateColors = {'g': green, 'y': yellow, 'r': red, 'b': blue, 'p': purple}
  translatePositions = {'d': down, 'r': right}
  color, position = items
  color = translateColors[color]
  position = translatePositions[position]
  if reverse:
    return ('%s%s' % (position, color)).decode('hex')
  else:
    return ('%s%s' % (color, position)).decode('hex')

from itertools import combinations
import re
p = re.compile(r'[^\w]')

hexList = '0123456789abcdef'
for colors in combinations(hexList, 5):
  for directions in combinations(hexList, 2):
    firstString = p.sub('', ''.join([encoder(light, colors+directions) for light in lights]))
    secondString = p.sub('', ''.join([encoder(light, colors+directions, reverse=True) for light in lights]))
    if len(firstString) == 11 or len(secondString) == 11:
      print colors+directions
      print "\t", firstString
      print "\t", '-'*20
      print "\t", secondString
      print '.'*30