wrestling-11 teams 4 mats 2 days 5 match limit

[waffen626]

I am organizing a high school team wrestling tournament where I have an odd number of teams (11).  I need to set up a round robin but there is one key hurdle...this event takes place over two days and high school rules state that each team may only wrestle 5 matches in a day.   We have 4 mats to work with.
 
So, my schedule needs to have everyone wrestle each-other and get 5 matches each day while minimizing byes. Can you help?  Thanks!

[Ian Wakeling]

Unfortunately there is no such schedule.  The argument goes as follows:

There are 55 matches to play in the round robin, 27 of these are played on day 1, the remaining 28 are played on day 2.  Consider the 28 matches on day 2, which involve 28*2=56 slots in which a team plays.  Within the rules, 10 of the 11 teams can each be assigned 5 slots each, but the remaining team must play in all 6 remaining slots if the round robin is to be completed in 2 days.

Here is an example of such a schedule:

 M1    M2    M3    M4
(I J) (B D) (E F) (---)
(B H) (D G) (C F) (A K)
(B E) (A I) (J K) (C D)
(A C) (F J) (G H) (B I)
(A G) (F H) (E K) (D J)
(C I) (E J) (B G) (A H)
(F K) (C G) (E I) (D H)
------------------------
(B K) (C H) (A D) (E G)
(D E) (H I) (A J) (B F)
(E H) (G K) (C J) (F I)
(H J) (D K) (A B) (C E)
(F G) (B J) (D I) (C K)
(D F) (A E) (H K) (G I)
(I K) (A F) (B C) (G J)

teams A to J play exactly 5 times each on both days, but team K plays 4 times on day 1 and 6 times on day 2.  Additionally each teams plays 2 or 3 times on each mat.

Hope that helps.

[waffen626]

Thank you It's so nice to know for sure and not keep second guessing myself, I had our whole math department working on it.  I think we will have to scrap the 11 team idea and move to ten in order to have a clear winner.   Would you be willing to generate a formula for the same criteria for 10 teams on 4 mats in 2 days with a 5 match limit per day?  Thank you so much!

[Ian Wakeling]

That's OK, I thought there might be no flexibility in the school rules, so here is a 10 team version.

 M1    M2    M3    M4 
(B I) (F G) (D H) (E J)
(A D) (B F) (C G) (---)
(A F) (D J) (C E) (H I)
(G J) (A H) (E I) (B D)
(A E) (---) (F J) (B C)
(B H) (D G) (I J) (A C)
------------------------
(G I) (C J) (A B) (E F)
(D I) (E H) (---) (B J)
(C D) (B E) (F H) (A G)
(E G) (C H) (A J) (F I)
(H J) (C I) (B G) (D F)
(C F) (A I) (D E) (G H)

There need to be 3 rounds where one of the mats is not used, so I have put these on different mats and at least one on each day.  Teams should wrestle 2 or 3 times on each mat, and any one team will have one bye on one of the days, and two byes on the other day.  Where a team has two byes, then they will not be consecutive.  Good luck with the tournament.

[waffen626]

Thank you.  Agian it is way nice to have your help. I am so fortunate to run across your site.  Thank you for your time, advice and sound program.