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This Python 3 program uses the

Football.substituted_table()function from theenigma.pylibrary to find possible match outcomes. Then it uses a recursive function to allocate scores to the matches that satisfy the goals (match points) for / against conditions. It runs in 133ms.Solution:The scores in Wales’ matches are: England vs. Wales = 3-0; Scotland vs. Wales = 3-3; Wales vs. Ireland = 4-4; Wales vs. France = 6-3.Each team scored 13 points overall.

There are 6 different ways to assign the scores, but the scores in the England vs. Scotland, England vs. Wales, Scotland vs. Wales, Wales vs. Ireland, Wales vs. France, and Ireland vs. France matches are always the same.

The scores in the matches that don’t involve Wales are:

England vs. Scotland = 0-0;

England vs. Ireland = 4-0 or 4-3 or 6-0;

England vs. France = 6-0 or 6-4 or 4-0;

Scotland vs. France = 6-4 or 6-0 or 4-0;

Scotland vs. Ireland = 4-3 or 4-0 or 6-0;

Ireland vs. France = 6-6.

Here’s a declarative solution in MiniZinc. It runs in 86ms.

If you want to see the six possible solutions you can remove the comments in the

outputclause to show all the scores.