S2T2

Jim Randell 9:48 am on 21 June 2020 Permalink Reply
Tags: by: R Postill ( 18 )   

• 

  Jim Randell 9:49 am on 21 June 2020 Permalink | Reply

  This Python program runs in 52ms.

  Run: [ @repl.it ]

  from enigma import subsets, intersect, diff, join, printf
  
  players = "LMNOPQRSTUVWXYZ"
  
  # generate possible 2nd XI's
  def generate():
    for ps in subsets(players, size=11):
  
      # verify conditions:
  
      # "U refused to play in the same team as Z"
      if 'U' in ps and 'Z' in ps: continue
  
      # "Q said that he would not be available if either L or M was picked"
      if 'Q' in ps and ('L' in ps or 'M' in ps): continue
  
      # "P announced that he would not turn out (a) unless M was in the
      # side, (b) if either O or W played"
      if 'P' in ps and ('M' not in ps or 'O' in ps or 'W' in ps): continue
  
      # "Z declined to play in an XI containing more than one of R, S, T"
      if 'Z' in ps and len(intersect((ps, "RST"))) > 1: continue
  
      # "V agreed to play only with Q"
      if 'V' in ps and 'Q' not in ps: continue
  
      yield ps
  
  # choose two sets for the second eleven
  for (s1, s2) in subsets(generate(), size=2, select="P"):
  
    # M is in the final set
    if 'M' not in s2: continue
  
    # the two promoted are in the first but not the second
    ps = diff(s1, s2)
    if len(ps) != 2: continue
  
    # the ones who were never picked
    ns = diff(players, s1 + s2)
    printf("promoted={ps} omitted={ns} [{s1} -> {s2}]", ps=join(ps), ns=join(ns), s1=join(s1), s2=join(s2))
  
  

  Solution: Q and V were promoted. P and Z were omitted.

  The original 2nd XI was: N O Q R S T U V W X Y.

  And then Q and V were promoted to the 1st XI. L and M stepped in to take their places.

  So the actual 2nd XI was: L M N O R S T U W X Y.

  P and Z were omitted from both line-ups.

  V will play only with Q, so it makes sense that Q and V were promoted together. (Although I didn’t check that the requirements for the 2nd XI were satisfied by the new 1st XI, but in this case they would be).

  These are the only two possible line-ups allowed for the 2nd XI for the given conditions, so the one with M in must be the actual line-up.

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• 

  John Crabtree 8:06 pm on 25 June 2020 Permalink | Reply

  Four players were initially not picked.
  From the two statements involving Z, if Z plays, U does not play and at least two of R, S and T do not play.

  The two statements involving Q may be written as:
  Q + ~Q.~V = 1
  Q.~L.~M + ~Q = 1
  Combining them gives Q.~L.~M + ~Q.~V = 1
  Either L and M do not play, or Q and V do not play, and so Z does not play,
  The statements involving P may be written as P.M.~O.~W + ~P = 1
  If P plays, Q, V, O, W and Z do not play. And so P does not play.

  And so Q and V were promoted. P and Z did not play.
  L and M were brought in to the 2nd XI as replacements.

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