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Programming Enigma Puzzles

15 February 2017

Posted by on **From New Scientist #1132, 7th December 1978** [link]

It was, I’m afraid, typical of Uncle Bungle that he should have torn up the sheet of paper which gave particulars of the numbers of matches played, won, lost, drawn and so on of four local football teams who were eventually going to play each other once. Not only had he torn it up, but he had also thrown away more than half of it onto, I suspect, the fire, which seems to burn eternally in Uncle Bungle’s grate. The tear was a vertical one and the only things that were left were the “goals against” and the “points” — or rather most of the points, for those of the fourth team had also been torn off.

What was left was as follows:

(2 points are given for a win and 1 for a draw).

It will not surprise those who know my uncle to hear that one of the figures was wrong, but fortunately it was only one out (i.e. one more or one less than the correct figure).

Each side played at least one game, and not more than seven goals were scored in any match.

Calling the teams

A,B,CandDin that order, find the score in each match.

[puzzle81]

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There’s not enough of the table (and one of the entries is wrong anyway) to make it worthwhile to use the

Football.substituted_table()solver from theenigma.pylibrary. But we can use other routines in theFootball()class.This Python program runs in 250ms.

Solution:The scores in the matches that have been played are: A v B = 3-3; A v D = 3-2; B v C = 1-0; B v D = 4-3.The remaining matches are not yet played.

The incorrect figure is the “goals against” column for C. It should be 1 (not 0).

This is what the full table looks like: