## Brain-Teaser 499

**From The Sunday Times, 20th December 1970** [link]

Paddy was in a reminiscent mood. “Sure it was a good year for Ireland, for didn’t we beat England by 4 goals to 1 and win the championship?” he said, proudly showing us the league table of the championship in which each country had played against each of the other three.

“Of course”, he added slyly, “you can now work out the score in one of the other matches”.

Which match? And what was the score?

[teaser499]

## Jim Randell 9:04 am

on10 September 2019 Permalink |This Python program uses the [[

`Football()`

]] helper class from theenigma.pylibrary. It runs in 95ms.Run:[ @repl.it ]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

on10 September 2019 Permalink |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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