Math problem

[geoschmo]

Originally posted by cybersol:
I have verified the following solution by Erax for 9 players. LGM, why do you think it does not work and why does your program fail to find it?

I suspect his program is hitting a point where it can't find a valid remaining set and is then deciding that number n has no solution. Whil ein fact as we showed earlier sometimes you can get stuck down a "blind-alley" where there is a solution for n, but not for every possible set of 3. Like what happened to Bbgemont. To completely rule out a possible solution it would have to back track when it reaches these end points and change an earlier set and rework from that point. Sounds complicated.

Geoschmo

[Gryphin]

(I don't really know anything about the math involved)
I did another google search:
"round robin tournament"
Then I tried:
"round robin tournament" +software

Quite a few hits that might help including calcuators.
Here is one link:
http://www.devenezia.com/downloads/round-robin/

I guess what I'm driving at here is others must have wanted this and their answer must be on the web.
Good luck

[ August 07, 2003, 00:58: Message edited by: Gryphin ]

[Captain Kwok]

Geo:

You have a difficult problem. Most programs used to set up match schedules like this are based on 2 players/teams.

What you are proposing is not a very common format to schedule and will be very difficult to organize. Other than finding the total number of games required (i.e. number of all the different combinations of players as calculated by others), you'll have to manually arrange the games or find someone to make a program for you that can do this automatically. On a more positive note, I'm sure there is some sort of combinations calculator out there on the net that lists each of the combinations...

[ August 07, 2003, 01:07: Message edited by: Captain Kwok ]

[Jack Simth]

Let's see: Floor function for the numbers:

Pp = players per game
Np = Number of players (total)
Gp = Games per player
Tg = Total games

Gp = (Np - 1) / (Pp - 1)
Tg = (Np * Gp) / Pp
= (Np*((Np - 1) / (Pp - 1)))/Pp
= (Np * (Np - 1)) / (Pp * (Pp - 1))

Gp = (Np - 1) / (Pp - 1)
Tg = (Np * (Np - 1)) / (Pp * (Pp - 1))

If Gp and Tg come out as positive integers, it should be doable - I'm not sure about the arrangement, however.

Edit: Arrangement method:

1) List players
2) Variables
Pp = players per game
Np = Number of players (total)
Gp = Games per player
Tg = Total games
Sk = Skip (counting variable; internal use only)
3) Gp = (Np - 1) / (Pp - 1)
4) Tg = (Np * (Np - 1)) / (Pp * (Pp - 1))
5) Sk = 0
6) Group, skipping Sk
7) Sk = Sk + Pp
8) If Sk < Np, Goto 6

[ August 07, 2003, 01:44: Message edited by: Jack Simth ]

[tesco samoa]

geo you should grab one of those wheel systems for lotteries.

you need a 3 of n wheeler with a filter

[cybersol]

Originally posted by Jack Simth:
Let's see: Floor function for the numbers:

Pp = players per game
Np = Number of players (total)
Gp = Games per player
Tg = Total games

Gp = (Np - 1) / (Pp - 1)
Tg = (Np * Gp) / Pp
...
If Gp and Tg come out as positive integers, it should be doable - I'm not sure about the arrangement, however.

I think this is the same as what I had a few Posts back, or am I missing something?

Edit: Oh sure add more

Originally posted by Jack Simth:
Edit: Arrangement method:
Edit: Arrangement method:

1) List players
2) Variables
Pp = players per game
Np = Number of players (total)
Gp = Games per player
Tg = Total games
Sk = Skip (counting variable; internal use only)
3) Gp = (Np - 1) / (Pp - 1)
4) Tg = (Np * (Np - 1)) / (Pp * (Pp - 1))
5) Sk = 0
6) Group, skipping Sk
7) Sk = Sk + Pp
8) If Sk < Np, Goto 6

Looks promising, but I don't understand exactly what you mean by group, skipping sk. Could you show the Np=13 and Pp=3 case I mentioned earlier as an example (since no one has shown it yet)?

[ August 07, 2003, 01:56: Message edited by: cybersol ]

[Captain Kwok]

Originally posted by tesco samoa:
geo you should grab one of those wheel systems for lotteries.

you need a 3 of n wheeler with a filter

This is exactly what he needs! Some sort of calculator that will list all the possible combinations of numbers (i.e. players) for n number of players, and r number of players per game!