Math Problem with Poker Application?
Posted by admin
I have 20 people lets call them:(ABCDEFGHIJKLMNOPQRST)
Now I want to conduct 20 DIFFERENT tournaments to place these players in:
Tournament 1 looks like this:
1.ABCDEFGHIJ
Tournament 2 looks like this:
2.KLMNOPQRST
Now my question is how do I arrange the letters in the next 18 tournaments so that:
1. No 2 tournaments are alike
2. Letters are EVENLY distributed so that players play against different competition each week.
Thanks.
I understand that there is no way to make it TOTALYY evn but I don’t want a lopsided configuration either…..
so if A plays B 6 times he may play T 4 times and so on…..
I think that if I can get it in that range it would acceptable but not A plays B 10 times and doesn’t even play T at all or 9 games to 1…….
July 19th, 2009 at 12:25 pm
Essentially you are choosing 10 letters from 20.
There are 20C10 = 184756 ways of doing that.
This covers every possible unique combination of 10.
Now you insist on 20 different tournaments. Actually each player only plays in 10 of those tournaments, each against 9 opponents. So in total he plays 90 opponents. But there are 19 other players total, which is not a factor of 90. So there is no way to get a purely even distribution. But’s it very easy to get unique tournaments. Just pick 20 out of the 184756.
*EDIT*
ARSBDIJMNO
How about this:
These are 10 groups of 10. For each number, the other tournament will be between the remaining 10 players.
1) APQBCDEFGH
2) APRBCEGIJK
3) APSCDFHJLM
4) APTDEGHKMN
5) AQRCFHILMO
6) AQSBCGJKLN
7) AQTEFHJKMO
9) ARTEFIKLNO
10) ASTBDGILNO