The first generalization of COUNTLESS 2D.

countless5.py

from itertools import combinations
from functools import reduce

def countless5(a,b,c,d,e):
  """First stage of generalizing from countless2d. 

  You have five slots: A, B, C, D, E

  You can decide if something is the winner by first checking for 
  matches of three, then matches of two, then picking just one if 
  the other two tries fail. In countless2d, you just check for matches
  of two and then pick one of them otherwise.

  Unfortunately, you need to check ABC, ABD, ABE, BCD, BDE, & CDE.
  Then you need to check AB, AC, AD, BC, BD
  We skip checking E because if none of these match, we pick E. We can
  skip checking AE, BE, CE, DE since if any of those match, E is our boy
  so it's redundant.

  Countless grows cominatorially in complexity.
  """
  sections = [ a, b, c, d, e ]

  p2 = lambda q,r: q * (q == r) # q if p == q else 0
  p3 = lambda q,r,s: q * ( (q == r) & (r == s) ) # q if q == r == s else 0

  lor = lambda x,y: x + (x == 0) * y # logical OR

  # important to use generator expressions here to reduce peak memory usage
  results3 = ( p3(x,y,z) for x,y,z in combinations(sections, 3)  )
  results3 = reduce(lor, results3)

  results2 = ( p2(x,y) for x,y in combinations(sections[:-1], 2) )
  results2 = reduce(lor, results2)

  return reduce(lor, ( results3, results2, e ))