Football League Tables - A proposed new problem

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CSFPython     2024-12-19 19:07:47

I was recently looking at a Football League Table and wondered what it might look like at the end of the season. I soon began to think about trying to calculate the number of different League Tables that could arise at the end of the season. Clearly there are some aspects of the problem that make it indeterminate. After removing these it soon became apparent that the final number was going to be extremely large. I ended up making a large number of simplifications in order to keep the final number within sensible bounds. Hopefully I have retained the more interesting aspects of the problem.

Rodion (admin)     2024-12-21 06:05:13
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Clive, thanks a lot for the puzzle! Sorry for delay.

I soon began to think about trying to calculate the number of different League Tables

So it happens not only in jokes about scientists but in real life also :)

Hopefully I have retained the more interesting aspects of the problem.

Looks like that! Though I haven't yet figured out whether this trick about specifying sum for two last teams makes significant simplification (we can specify sum of 0 for 0 last teams seemingly and problem remains the same?) And as a bonus the problem description is very good for learning some popular terms used in this popular game :)

CSFPython     2024-12-21 10:36:38

Rodion,

Thanks for posting the problem. Specifying the points scores for the bottom two teams is only a simplification in that it produces a large reduction in the number of possible League Tables. However, the same reduction could be achieved by using 21 teams rather than 23. Unfortunately this would mean that we get the same problem every time it is set. The main reason for specifying the bottom two teams is that this gives a choice of more than 1000 different problems.

gardengnome     2024-12-21 14:55:15
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This was needed after the craziness of AOC day 21. Thank you.

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