S2T2

Jim Randell 8:54 am on 2 March 2019 Permalink Reply
Tags: by: R Brain ( 3 )   

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  Jim Randell 8:55 am on 2 March 2019 Permalink | Reply

  The enigma.py library includes the [[ Football() ]] class to help in solving puzzles involving football tables, and the [[ filter_unique() ]] function to help in solving puzzles of the form “… if I told you this, then you could work out that…”. We can use both of these to solve this puzzle.

  This Python program runs in 98ms.

  Run: [ @repl.it ]

  from enigma import Football, filter_unique, unpack
  
  # record possible outcomes
  rs = list()
  
  # scoring system
  football = Football(games='wdl')
  
  # the order of the teams in the table
  (B, A, P, E) = (0, 1, 2, 3)
  
  # digits in the table stand for themselves
  d = dict((x, int(x)) for x in "01234789")
  
  # the columns of the table
  (table, gf, ga) = (dict(w="3100", d="0121", l="0112"), "9724", "3847")
  
  # find possible match outcomes
  for (ms, _) in football.substituted_table(table, d=d):
  
    # find possible scorelines using the goals for/against columns
    for ss in football.substituted_table_goals(gf, ga, ms, d=d):
  
      # record outcomes
      rs.append((ms, ss))
  
  # if I told you...
  # the number of scores of 1 goal by either side in the games played by B...
  f = unpack(lambda ms, ss: sum(v.count(1) for (k, v) in ss.items() if B in k))
  
  # you can deduce the scores in the AvP and AvE match
  g = unpack(lambda ms, ss: (ss[(A, P)], ss[(A, E)]))
  
  # find the unique solutions
  (rs, _) = filter_unique(rs, f, g)
  
  # output solutions
  for (ms, ss) in rs:
    football.output_matches(ms, ss, "BAPE")
  

  Solution: A vs P = 1-1. A vs E = 5-3.

  The scores in all matches are uniquely determined. They are:

  B vs A = 4-1
  B vs P = 3-1
  B vs E = 2-1
  A vs P = 1-1
  A vs E = 5-3
  P vs E = 0-0

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