Math problem

[tesco samoa]

i posted this earlier

i have a question along this line

say you have 24 numbers and you want to sort them in combinations of 4 where each number only appears once with each other how many combinations would that be ???

now if some one wanted to whip up a little program that does that ( but i can select the numbers (say up to 50), combinations ( 2 to 12 ) and uniqueness ( say once to 6 times ) and can produce a text file output i would be forever thankful

And in VB and send me the source

[Ack]

The only hard part about that would be using VB. I switched to Perl and haven't used anything else in about 2 years.

Oh yeah. I believe the even equation is simply:

Pg = players per game
n = total number of players

# games = [(1/Pg) Summation (A=1 to A=n)] + 1

[Ack]

Duh! Algorithm.

1. Drop each combination into an array of n elements. Where n is the number of players per game.
2. Sort each array numerically.
3. Compare each array to the next and discard in duplications.
4. Output the remaining arrays into a text file.

Ugly and inefficient, but a P4 should make short work of it.

[LGM]

I guess I missed Erax's solution for 9 players. To appears that how you pick your combinations matters. My alogorythm finds combinations in a certain manner so it only works for certain numbers. A different method might find other solutions.

An exhaustive method would build all combinations and start eliminating redundant combaintions and each iteration it would pick a different combination of redundants to eliminate. This makes the problem even messier.

I tried doing 9 on paper myself and I couldn't do it. Probably because I did it much the same way I programmed it.

Good news for Geosmo is we have known solutions now for 7,9,15, and 31. Maybe someone else can figure out solutions for 11, 13, 17, 19, ...

I know the even numbers will not work because player 1 must play every other player in three player games. Therefore the number of players opposing player one must be a multiple of 2. Adding in player 1 makes the total number of players an Odd number.

[ August 07, 2003, 15:41: Message edited by: LGM ]

[LGM]

I had an SEIV turn to do Last night (my gracious host is running turns manually while PBW is down). Maybe tonight I can tackle writting a program to find combinations for Geo.

It is an interesting problem. This time I will probably write it in Delphi and make it a Windows executible. I'll need to arrange my data a bit better to back track when I get stuck down a blind alley looking for a solution.

I'll publish the code. Delphi code should be fairly easy for C++ or Java programmers to understand as the language is somewhat similiar.

[Erax]

I tried doing 9 on paper myself and I couldn't do it. Probably because I did it much the same way I programmed it.

I did it graphically. I set the players up like this :

1 2 3
4 5 6
7 8 9

Then connected them first horizontally, then vertically, then along the diagonals (you have to imagine that the numbers 'wrap around' for the diagonals). To my surprise, this solved it for nine players.

[tesco samoa]

http://www.singlix.com/download/combinator.html

has the source code for the routine that determines pairing of numbers

It is in turkish but stepping though it will be ok