Round Robin Tournament Scheduling

Field Day!!

Amanda_Young · 6 · 3751

Amanda_Young

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on: April 25, 2013, 11:00:11 PM
I have 9 teams and can have 8 or 9 stations. Stations can be split into two rounds. The "bye" round willl be a rest station because of odd # of teams!!

Ideally each team would play eachother, but most importantly, each team will have a turn at each station.

Please help!!


Ian Wakeling

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Reply #1 on: April 26, 2013, 02:43:03 AM
If you were to lose one team, or find an extra team, then things would be perfect as you could either use this schedule for 7 stations or the schedule for 9 stations below.  But as stated the problem has no solution.  You are trying to arrange 36 matches in 9 rounds with 8 stations.  Each round must have 4 matches, however 4 of the stations must have 5 matches and the other 4 stations must have 4 matches (4*5 + 4*4 = 36), so there must be at least one team that has not played at each of the latter 4 stations (and also at least one team that has played twice at the former 4 stations).  If a 9th station (not a bye station) is added, then all stations must have exactly 4 matches and there will be at least one team who has not played at each station (to obtain such a schedule delete all the matches involving team J below).

(I A) (---) (G C) (---) (J H) (D E) (---) (F B) (---)
(---) (C B) (---) (---) (A D) (H F) (J G) (---) (I E)
(---) (E J) (D F) (I G) (---) (---) (B H) (C A) (---)
(H G) (---) (E A) (D B) (F C) (---) (---) (I J) (---)
(J F) (H D) (---) (---) (G E) (I C) (---) (---) (B A)
(---) (I F) (---) (A H) (---) (B G) (E C) (---) (J D)
(D C) (---) (---) (---) (I B) (A J) (---) (H E) (G F)
(E B) (---) (I H) (C J) (---) (---) (F A) (G D) (---)
(---) (A G) (B J) (F E) (---) (---) (I D) (---) (C H)


Amanda_Young

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Reply #2 on: April 24, 2014, 12:13:42 AM
Okay it's this time again. This time we have 10 teams, and 10 stations! Please help!
Thanks!


Ian Wakeling

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Reply #3 on: April 24, 2014, 02:34:08 AM
It will work much better if you can reduce the number of stations to 9, then everyone can have all 9 opponents and play once at each station.  See the schedule above.
« Last Edit: April 24, 2014, 07:35:04 AM by Ian »


kbarnes90

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Reply #4 on: June 01, 2015, 11:39:21 PM
The schedule above includes 10 teams and 9 stations.  Is there a way to do it with 9 teams and either 8, 9 or 10 stations?  Our field day is the day after tomorrow and I'm stumped on this one.  We've already announced teams so I'll be hard to add or remove a team and we really want everyone to play every game. Thanks so much for your help!!!!


Ian Wakeling

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Reply #5 on: June 02, 2015, 02:07:13 AM
There is no balanced solution when there is an odd number of teams.  The only suggestion I have would be to use the schedule above but remove every game that involves team J.  This will leave you with a schedule where every teams plays at 8 of the 9 stations and where every team has one bye round.