S2T2

Jim Randell 9:03 am on 10 September 2019 Permalink Reply
Tags: by: David W Poyner   

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  Jim Randell 9:04 am on 10 September 2019 Permalink | Reply

  This Python program uses the [[ Football() ]] helper class from the enigma.py library. It runs in 95ms.

  from enigma import (Football, digit_map, Accumulator, printf)
  
  # scoring system
  football = Football(games='wdl')
  
  # labels for the teams (in table order)
  order = (I, W, E, S) = (0, 1, 2, 3)
  teams = "IWES"
  
  # values stand for themselves
  d = digit_map(0, 9)
  
  # columns of the table
  (table, gf, ga) = (dict(w="3110", d="0101", l="0122"), "9565", "3589")
  
  # known matches
  (ms0, ss0) = ({ (I, E): 'w' }, { (I, E): (4, 1) })
  
  # find scores common to each scenario
  r = Accumulator(fn=lambda s, v: s.intersection(v))
  
  # find possible match outcomes
  for (ms, _) in football.substituted_table(table, d=d, matches=ms0):
  
    # find possible scores
    for ss in football.substituted_table_goals(gf, ga, ms, d=d, scores=ss0):
  
      # output scenario
      football.output_matches(ms, ss, teams=teams)
  
      # record scores
      r.accumulate(set(ss.items()))
  
  # output fixed scores (other than for I vs E)
  printf("SOLUTION:")
  for ((x, y), (sx, sy)) in r.value:
    if (x, y) == (I, E): continue
    printf("-> {x} vs {y} = {sx}-{sy}", x=teams[x], y=teams[y])
  

  Solution: The score in the Wales vs Scotland match must be 2-2.

  There are 5 different scenarios for the scores, but in each of them W vs S is 2-2.

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  • 

    John Crabtree 3:39 pm on 10 September 2019 Permalink | Reply

    As league table puzzles go, this is an easier one.

    If the score in IvW is x – y, and the score in WvS is d – d, the other scores are:
    IvS (5 – x) – (2 – y)
    WvE (5 – d – y) – (5 – d – x)
    EvS (d + x) – (d + y – 1)

    Looking at the goals scored by Scotland, 5 = d + (2 – y) + (d + y – 1) = 2d + 1, ie d = 2

    And so the score in Wales v. Scotland is 2 – 2

    By inspection, the possible values for (x,y) are (1, 0), (2, 1), (2,0), (3, 1), and (3, 2)

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