Permutations - I think

SlinkyFinky · 2012-02-24 08:04:02

A friend was organising a quiz party for his mates. There were 24 people participating and to avoid over competitiveness he arranged each round so that each team had different players. No 2 players were ever in the same team. He planned 4 rounds with either 6 teams of 4, or 4 teams of 6. He figured it all out by constructing matrices. I would like to how to solve this mathematically. X players Y teams Z rounds no 2 players ever in same team.

Also if say some number other that 24 turned up how could he adjust the size of teams and number of rounds to accommodate?

How? Pleased if you can help

bobbym · 2012-02-24 08:23:22

Hi SlinkyFinky;

Welcome to the forum!

He may have used matrices to represent them but as far as I know he did not use matrices to solve them.

This is called a "social golfers problem" or "progressive dinner". I can direct you to some good links. The problem is solved by a computer. Some arrangements can not be done.

Label your people A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X

SlinkyFinky · 2012-02-25 03:24:39

What a pleasant surprise receiving your reply (and so quickly)

I would love to see the links that would show me how it's done. Is there any underlying mathematical techniques. Surely it's not just trial and error/exhaustion.

thanks

bobbym · 2012-02-25 08:19:12

Hi;

I would love to see the links that would show me how it's done. Is there any underlying mathematical techniques. Surely it's not just trial and error/exhaustion.

Unfortunately, it seems to be just a computer problem. Try here

http://www.maa.org/editorial/mathgames/ … 14_07.html

http://www.cs.brown.edu/~sello/golf.html

http://www.cs.brown.edu/~sello/uniques.html

http://www.csplib.org/prob/prob010/index.html

http://faculty.mercer.edu/schultz_sr/so … olfer.html

SlinkyFinky · 2012-02-26 12:04:30

Well thanks bobbym. I'll go and have a look at the links. It's strange that my mate is both big at golf and has worked in computers all his life. I hope I don't sound ungrateful, but I'm sure someone had to write the computer programme that solves the problem. So they must have had some idea how to solve it. For example could someone compute the odds of the second round where no two people from round 1 were in the same team and so on. I'm not ungrateful, it's just hard to believe that there isn't a numerical technique that is the equivalent of arranging 24 tiles so that they obeyed some rules.

Anyway thanks again. I'll write after I've looked at the links.

SlinkyFinky · 2012-02-26 12:21:25

Bobbym, you could knock me down with a feather. I've just looked at the first link. I knew a guy years ago and he got a first in combined maths and astronomy. (around 1985) He told me he discovered something in maths. He told me it was to do with the Steiner Triple Series. I'd never heard of it, but he told me that in the Steiner Triple Series certain patterns were never supposed to repeat and he wrote a computer programme which showed they did. You can imagine 25 years on it was an amazing coincidence to come across this mysterious sounding maths jargon.
I shall read on with relish.
Thanks again

bobbym · 2012-02-26 14:14:02

Hi SlinkyFinky;

There are definitely methods but they seem to be computer methods. You can write a computer program to solve many types of problems that are very difficult or impossible using mathematics. Take the TSP, there are computer techniques but no mathematical method to solve it.

Math Is Fun Forum

#1 2012-02-24 08:04:02

Permutations - I think

#2 2012-02-24 08:23:22

Re: Permutations - I think

#3 2012-02-25 03:24:39

Re: Permutations - I think

#4 2012-02-25 08:19:12

Re: Permutations - I think

#5 2012-02-26 12:04:30

Re: Permutations - I think

#6 2012-02-26 12:21:25

Re: Permutations - I think

#7 2012-02-26 14:14:02

Re: Permutations - I think

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