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Programming Enigma Puzzles

16 November 2016

Posted by on **From New Scientist #1140, 1st February 1979** [link]

I am Sergeant Simple and I keep the notes and diaries,

Of my boss Professor Knowall, magic name;

I do all the donkey work and help in the inquiries,

So the Prof. can close his eyes and use his brain.But it is not only crime which occupies his mind,

For we also follow soccer here and there,

And I will tell you now of a most important find

Which made a nonsense problem crystal clear.This is soccer for a few,

By a method which is new,

Ten and five are points awarded for a win and for a draw,

And a point for every goal that has been scored.If you ask what this is for

I reply that that’s the lawAnd more goals will be obtained as the reward.

Four teams all played each other, it does not matter when,

AandCgot eight points each andBnineteen, and then

One more got fifty seven. And there’s a problem rich

For one teams points are incorrect. I must not tell you which.But Professor Knowall knows and he says this:

“If I give the information that you can discover which,

Why then you will be able so to do”.The Professor, as we know, is good at many things,

But he has not got the fantasy that gives a poet wings.

Two bits of information that will help you in your approach

And you can then the puzzle solve. For when

A match is played at least one goal is scored by both,

But they never scored together more than ten.Which figure was wrong? And what information can you give about the score in each match?

[puzzle88]

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I’m not entirely happy with this puzzle. I think the crux is deciphering the phrase: “If I give the information that you can discover which, Why then you will be able so to do”. Which I suppose is meant to tell us that the wrong total cannot be A or C. There is nothing in the puzzle text to distinguish A and C, so for any solution that involves A there will be a corresponding solution involving C where the labels for A and C are swapped.

This means we only need to consider B and D as the incorrect scores.

This Python program uses the

Football()helper class from theenigma.pylibrary to consider possible match outcomes. It runs in 991ms.Solution:The score for B was wrong.The score for B should be between 25 and 39.

There are 64 different ways to achieve this:

Possible scores are:

The 8 possibilities for A vs B multiplied by the 8 possibilities for B vs C give the 64 possible combinations.

If the scores for either A or C were wrong there would be 109 possible sets of match outcomes in each case.