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Programming Enigma Puzzles

24 October 2013

Posted by on **From New Scientist #2540, 25th February 2006**

Our local football team consists of five teams and in the course of the season each team plays each of the others once. One point is awarded to each team for a draw and a higher whole number of points (I forget how many) are awarded for a win. Below is part of the league table sometime during the season before all the matches had been completed.

The teams are shown in alphabetical order rather than order of merit. No teams have the same number of points. In the table, digits have been replaced consistently by letters, with different letters used for different digits.

How many points for a win? Which team or teams (if any) have the Authors beaten so far?

**Enigma 1559** is also called “Points for a win”.

[enigma1380]

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This Python program uses the [[

`Football()`

]] class, recently added to theenigma.pymodule. It looks at the possibilities for the “Won”, “Lost”, “Drawn”, “Points” and “Position” columns, and then goes on to verify that are possible score lines corresponding to the games that would make the “Goals for” and “Goals against” columns work. It runs in 469ms.Solution:4 points are awarded for a win. The Authors have beaten The Editors.There are many possible score lines for the games, but in all cases the answers to the questions in the problem statement are the same.