## Brain-Teaser 468

**From The Sunday Times, 17th May 1970** [link]

In a home association football championship, where each of the four countries plays the others once, the teams were very evenly matched. The result was that all four countries gained the same number of points and all had the same goal average.

England were the highest scorers in any one match, scoring 6 when beating Northern Ireland, and this also proved to be the match with the greatest number of goals. Second highest scorers were Northern Ireland, scoring 5 when beating Scotland, but there were more goals in their match with Wales when they scored 4.

In order to decide the champions the team scoring the highest number of goals in the championship were adjudged the winners. There was one outright winner with only 2 goals separating the top and bottom teams.

What was the aggregate number of goals for each team?

[teaser468]

## Jim Randell 9:30 am

on2 April 2019 Permalink |Using the [[

`Football()`

]] helper class from theenigma.pylibrary we can find a solution to this puzzle.I assumed that 2 points were awarded for a win, and 1 for a draw. (With 3 points for a win there is no solution).

This Python program runs in 295ms.

Run:[ @repl.it ]Solution:Northern Ireland scored 12 goals. Wales scored 11 goals. England and Scotland each scored 10 goals.There is only one set of match outcomes that gives the required result:

Each team ends up with 3 points (E, N, S from 1w+1d, W from 3d), and with the same number of goals for and against (giving a goal average of exactly 1).

LikeLike