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    • Football going into Football Net

      League table teasers

      21 June, 2011

      This puzzle is from the excellent book The hidden mathematics of sport by Rob Eastaway and John Haigh, reproduced here with kind permission of the authors.

      football

      Football tables have been the basis of many a brainteaser over the years. These two puzzles ask you to work out what the scores were in all matches played so far this season.

      Puzzle 1: Each team played the others once, what were the scores in each match (2 points for a win, 1 for a draw)?

      PlayedGoals forGoals againstPoints
      United2103
      City2212
      Albion2021

      Puzzle 2: The league table below got smudged in the rain, and is only partly legible. Eventually each team will play the others once, but the tournament isn't over yet. Can you find all the results?

      PlayedWonLostDrawnGoals forGoals against Points
      Athletic32**4 4*
      Rovers*1*03 0*
      Town***01 1*
      Wanderers***** **

      Both puzzles require a degree of deductive reasoning. One way to begin to tackle them is to realise that, for example, the total of the Win column is always the same as the total of the Lose column (one win for one team must create one loss for another team), while the total of the Draw column will be twice the number of matches that have been drawn (because every draw involves two teams). Similarly, the Goals for and Goals against columns must add up to the same total.

      Solution link
      League table teasers - solution
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      Anonymous

      27 January 2013

      Permalink
      Comment

      Puzzle 1:

      United Vs City 1-0
      United Vs Albion 0-0
      City Vs Albion 2-0

      Puzzle 2:

      Athletic 3 2 1 0 4 4 4
      Rovers 1 1 0 0 3 0 2
      Town 2 1 1 0 1 1 2
      Wanderers 2 0 2 0 1 4 0

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