Am I asking for the impossible?

[Mike Von]

Ian,

I searched the site but couldn't find:

eight players
doubles tennis
three rounds
only play against a player once
the one player you don't play against, you have as a partner once during the 3 rounds

Is there a solution that meets these requirements?

Any help is much appreciated.

[Mike Von]

Ian,

I forgot to specify 2 courts.

Thanks,
Mike

[Ian Wakeling]

Unfortunately, no such schedule exists. You can have a schedule where the one player who you don't play against is not a partner.  This is the spouse avoiding schedule for 8 players.

[Mike Von]

Ian,

Thank you very much for getting back to me.

The "Spouse Avoiding" schedule is hilariously named and could be very helpful.

Mike

[markyb610]

Ian,

I can see you've done some fantastic work here. I was looking at your 32 player round robin and it's so nearly what I'm looking for. I can see you rely on there being eight courts.

Would it be possible to generate a six court solution ? (So presumably with 10 matches per court - 8 matches per player and two byes per person) ??

Many thanks
Mark

[markyb610]

Ian,

I should have said this is for doubles (or perhaps it was obvious !).

Other solutions on the web don't seem to provide the goal of as few "duplicates" (partners & opponents) as you have managed so well !

Many thanks
Mark 

[Ian Wakeling]

"(So presumably with 10 matches per court - 8 matches per player and two byes per person) ?"

I am confused about the numbers here.  There are 8 byes per round. So for everyone to have the same number of games, there needs to be a multiple of 4 matches per court.  For example 8 matches per court would be two byes per person.  Is that what you want?

[markyb610]

Ian,

Quite right !  I can see that 10 rounds would require a mix of 7 or 8 to be played by all players. My mistake.

So I think my (corrected) requirement is  . . . 

6 courts          12 rounds         32 players - playing in random doubles each round

Total matches played = 72 ( 6 courts x 12 rounds)

Therefore 72 x 4 = 288 = individual scores/results

3 byes per player - so 9 matches per player (12 rounds - 3 byes) will count towards the result

In each round there will be 8 byes ( Total players less doubles on all courts = 32 - (4 x 6) )


Many thanks
Mark

[Ian Wakeling]

Mark,

Here is a schedule that might be useful.

( 9 26 v 32  5)  ( 1  8 v 15  7)  (17  4 v 31 12)  (13 29 v  3 19)  (14 20 v 30 10)  (21  6 v 11  2)
(28  6 v 29  7)  (11  5 v 18  4)  (15 13 v 32 24)  ( 9 21 v 31  3)  (20 23 v 26  2)  (19  8 v 25 22)
( 8 21 v 30 27)  (26 28 v  1 18)  ( 7 31 v 19 14)  (17  5 v 13  2)  (11 29 v  9 24)  (12 16 v  6 25)
( 1 11 v 29 10)  (25  9 v  4 23)  ( 2  6 v 15 22)  ( 3 16 v 26  7)  (18 28 v 24 30)  (21 14 v 12 32)
(23 22 v  1 27)  ( 5 19 v 16 20)  (30 15 v 12  7)  (26 29 v 17 21)  (32 28 v  4  2)  (31  8 v 24 10)
( 2  9 v 19 30)  (25 12 v  3 11)  (27 14 v  6 24)  (18 17 v 32 10)  (22 28 v 20 31)  (29 15 v  5 16)
(32 15 v 23 19)  (13  6 v 31 26)  ( 5 10 v  3 22)  (18 29 v 27 25)  ( 1  2 v 14  9)  ( 4  8 v 16 17)
(11  8 v 31 23)  (13 30 v 25  1)  (27 10 v  9 16)  ( 4 22 v 14 29)  (24 12 v 19 26)  (21 20 v 18 15)
(10  6 v  4 19)  ( 1  3 v 32 20)  (30 11 v 26 27)  ( 7 24 v 23 17)  (18 22 v  9 12)  (28  8 v 13 14)
(17  3 v  1  6)  (27 12 v 28  5)  (24 20 v  7  4)  (16 31 v  2 18)  (15 26 v 25 14)  (23 10 v 13 21)
(11 19 v 17 28)  (25  7 v  5 21)  ( 4 20 v 27 13)  (30 22 v 32 16)  (29  2 v  8 12)  (23 18 v 14  3)
(30  5 v  6 23)  (27 31 v 25 32)  (13  7 v 11 22)  ( 3 10 v 15 28)  (20  9 v  8 17)  ( 1 24 v 21 16)

All the partners are different, and all the opposition pairs are different, but there are about 17 pairs who meet twice.  I am sure it's possible to do better, but the problem is that my software is not optimized for this scenario.

[markyb610]

Ian,

That's amazing - Perfect !!

Many thanks   - and so quick too !
Mark

[Mike Von]

Ian,

I searched the site but couldn't find:

doubles tennis, changing partners and opponents every round
3 courts
8 rounds
player numbers can be 13, 14, 15, 16
play with a player a maximum of one time
minimize the number of times you play against any player

Are there any solutions that meets these requirements?

Any help is much appreciated.

[Ian Wakeling]

Here are some possibilities for your 8 round schedule - the 16 player one is best since everyone has the same number of games.


13 players (players 1 to 5 play in every round, the others each have one bye)

( 5 12 v  7  8)  (11  4 v 10  6)  ( 3  9 v  1  2)
( 9  5 v 13 10)  ( 8  4 v 11  1)  ( 2  3 v  7  6)
(12  3 v  2  9)  ( 7 13 v  1  4)  ( 5  6 v  8 10)
( 5  2 v  9 11)  (13  6 v  1  7)  ( 8 12 v  3  4)
( 1 12 v 11 10)  ( 8  6 v 13  3)  ( 4  2 v  7  5)
(11  2 v  4 13)  ( 9 10 v  3  7)  ( 1  5 v  6 12)
( 5  3 v 11 13)  (10  2 v  1  8)  ( 4  6 v  9 12)
( 1  3 v  5  4)  ( 7  9 v 11  8)  (13  2 v 12 10)

14 players (players 13 & 14 have 6 games, the others have 7 games)

( 8 12 v 11  3)  ( 7  1 v  5  2)  ( 6  9 v  4 10)
( 2  3 v 10  5)  ( 6  8 v 14 13)  ( 1  9 v  7  4)
(12  3 v  6  7)  ( 2 14 v 11  4)  (13  8 v  5  1)
(11 12 v  1 10)  (14  4 v  5  3)  ( 9 13 v  2  6)
( 1 11 v  9  3)  (10  7 v  8 14)  (13  2 v 12  4)
( 1  2 v  6 14)  ( 9  8 v  7 12)  (11  5 v 10 13)
(12  9 v  5 14)  (13  7 v 10  3)  ( 4  6 v 11  8)
( 9  2 v  8  3)  ( 6 11 v  7  5)  (12 10 v  4  1)

15 players (players 1-9 have 6 games, players 10-15 have 7 games)

(13  5 v  7 12)  (10  8 v 11 15)  ( 4  6 v  9 14)
(15  1 v 12 14)  ( 3  8 v 10 13)  ( 2 11 v  7  9)
(11  1 v  2 15)  (12  6 v  4 10)  (14  5 v  3 13)
(15 13 v  6  2)  ( 5  3 v  1  9)  (14  4 v  8  7)
( 1 12 v  9  8)  ( 5  4 v 10  2)  ( 3  6 v  7 11)
( 5 12 v  6 11)  ( 9 13 v 10 15)  ( 8  2 v  3 14)
(11  9 v 14 13)  ( 4 12 v  3 15)  ( 6 10 v  1  7)
( 5  7 v  8 15)  ( 1  4 v 11 13)  (14  2 v 10 12)

16 players (all players have 6 games)

(15 12 v 16  8)  ( 6  5 v 14  9)  ( 7 11 v 13 10)
( 9 11 v 12  2)  (16 10 v 14  4)  ( 1  3 v 13 15)
(14  3 v  1  8)  (15  4 v  7  6)  ( 2 16 v  5 13)
( 2  6 v  3 10)  ( 1 11 v  9  4)  ( 8 12 v  5  7)
( 6 16 v 11  8)  (12  3 v 10  4)  (14  2 v  7 15)
(13  4 v  5  8)  ( 7  3 v  9 16)  (11 12 v  1 15)
( 1 10 v 16  5)  ( 6 14 v 13 12)  ( 2  9 v  4  8)
(13  9 v 15 10)  ( 7  2 v  1  6)  ( 5 14 v 11  3)


Hope that helps,

Ian

[Mike Von]

Ian,

You are amazing!



Thank you very much, our little tournament will run smoothly now.

Mike