Mixed Doubles Tennis with 30 Players

[Racquetball]

First let me say, "What a great website!"  Last night I found a mixed doubles tennis schedule on this site where partners rotate for 32 players.  We have a doubles racquetball league with 15 "A" players and 15 'B" players.  Is there anyway to create a similar mixed doubles rotating schedule with 30 players?


Below I have included the 32 player schedule so that you will understand what I am looking for.  I would imagine the 30 player schedule is impossible.

Thanks for yor help,

Steve Schwankhaus



Ian Wakeling
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Gender: male
Re: 26 players horseshoies
Reply #4 - 05/20/10 at 04:26:26 Quote  Yes, this is possible.  The problem has been studied by mathematicians since the 1970s, originally in the context of mixed doubles tennis for a club in NY State. There is a slight imbalance in the problem owing to the fact that there are 15 possible opponents of the same sex, but 16 possible partners/opponents of the opposite sex.  This is usually solved by making a spouse avoiding mixed doubles round robin, so in the schedule below the men are M1 to M16 and the women are F1 to F16.  The spouse pairs (M1 F1), (M2 F2), etc. never meet as partners or opponents, but otherwise the schedule meets your requirements above.
 
Round 1
(M1 F4 v M2 F3)
(M3 F2 v M4 F1)
(M5 F8 v M6 F7)
(M7 F6 v M8 F5)
(M9 F12 v M10 F11)
(M11 F10 v M12 F9)
(M13 F16 v M14 F15)
(M15 F14 v M16 F13)
 
Round 2
(M1 F7 v M3 F5)
(M2 F8 v M4 F6)
(M5 F3 v M7 F1)
(M6 F4 v M8 F2)
(M9 F15 v M11 F13)
(M10 F16 v M12 F14)
(M13 F11 v M15 F9)
(M14 F12 v M16 F10)
 
Round 3
(M1 F6 v M4 F7)
(M2 F5 v M3 F8)
(M5 F2 v M8 F3)
(M6 F1 v M7 F4)
(M9 F14 v M12 F15)
(M10 F13 v M11 F16)
(M13 F10 v M16 F11)
(M14 F9 v M15 F12)
 
Round 4
(M1 F13 v M5 F9)
(M2 F14 v M6 F10)
(M3 F15 v M7 F11)
(M4 F16 v M8 F12)
(M9 F5 v M13 F1)
(M10 F6 v M14 F2)
(M11 F7 v M15 F3)
(M12 F8 v M16 F4)
 
Round 5
(M1 F16 v M6 F11)
(M2 F15 v M5 F12)
(M3 F14 v M8 F9)
(M4 F13 v M7 F10)
(M9 F8 v M14 F3)
(M10 F7 v M13 F4)
(M11 F6 v M16 F1)
(M12 F5 v M15 F2)
 
Round 6
(M1 F11 v M7 F13)
(M2 F12 v M8 F14)
(M3 F9 v M5 F15)
(M4 F10 v M6 F16)
(M9 F3 v M15 F5)
(M10 F4 v M16 F6)
(M11 F1 v M13 F7)
(M12 F2 v M14 F8)
 
Round 7
(M1 F10 v M8 F15)
(M2 F9 v M7 F16)
(M3 F12 v M6 F13)
(M4 F11 v M5 F14)
(M9 F2 v M16 F7)
(M10 F1 v M15 F8)
(M11 F4 v M14 F5)
(M12 F3 v M13 F6)
 
Round 8
(M1 F2 v M9 F10)
(M2 F1 v M10 F9)
(M3 F4 v M11 F12)
(M4 F3 v M12 F11)
(M5 F6 v M13 F14)
(M6 F5 v M14 F13)
(M7 F8 v M15 F16)
(M8 F7 v M16 F15)
 
Round 9
(M1 F3 v M10 F12)
(M2 F4 v M9 F11)
(M3 F1 v M12 F10)
(M4 F2 v M11 F9)
(M5 F7 v M14 F16)
(M6 F8 v M13 F15)
(M7 F5 v M16 F14)
(M8 F6 v M15 F13)
 
Round 10
(M1 F8 v M11 F14)
(M2 F7 v M12 F13)
(M3 F6 v M9 F16)
(M4 F5 v M10 F15)
(M5 F4 v M15 F10)
(M6 F3 v M16 F9)
(M7 F2 v M13 F12)
(M8 F1 v M14 F11)
 
Round 11
(M1 F5 v M12 F16)
(M2 F6 v M11 F15)
(M3 F7 v M10 F14)
(M4 F8 v M9 F13)
(M5 F1 v M16 F12)
(M6 F2 v M15 F11)
(M7 F3 v M14 F10)
(M8 F4 v M13 F9)
 
Round 12
(M1 F14 v M13 F2)
(M2 F13 v M14 F1)
(M3 F16 v M15 F4)
(M4 F15 v M16 F3)
(M5 F10 v M9 F6)
(M6 F9 v M10 F5)
(M7 F12 v M11 F8)
(M8 F11 v M12 F7)
 
Round 13
(M1 F15 v M14 F4)
(M2 F16 v M13 F3)
(M3 F13 v M16 F2)
(M4 F14 v M15 F1)
(M5 F11 v M10 F8)
(M6 F12 v M9 F7)
(M7 F9 v M12 F6)
(M8 F10 v M11 F5)
 
Round 14
(M1 F12 v M15 F6)
(M2 F11 v M16 F5)
(M3 F10 v M13 F8)
(M4 F9 v M14 F7)
(M5 F16 v M11 F2)
(M6 F15 v M12 F1)
(M7 F14 v M9 F4)
(M8 F13 v M10 F3)
 
Round 15
(M1 F9 v M16 F8)
(M2 F10 v M15 F7)
(M3 F11 v M14 F6)
(M4 F12 v M13 F5)
(M5 F13 v M12 F4)
(M6 F14 v M11 F3)
(M7 F15 v M10 F2)
(M8 F16 v M9 F1)

Last Edit: 05/20/10 at 06:25:33 by Ian Wakeling

[Ian Wakeling]

Hi Steve,

Thanks for your message.  It's good news, since 30 players is possible, for example:

(H02 W03):(H08 W12) (H10 W02):(H14 W08) (H09 W01):(H06 W04) (H04 W10):(H11 W06) (H01 W09):(H15 W07) (H13 W14):(H03 W15) (H12 W13):(H07 W11)
(H06 W14):(H07 W10) (H12 W04):(H15 W06) (H11 W05):(H08 W09) (H01 W11):(H14 W03) (H10 W08):(H02 W15) (H09 W07):(H05 W02) (H04 W12):(H03 W01)
(H07 W01):(H15 W03) (H06 W11):(H03 W08) (H01 W07):(H02 W12) (H09 W04):(H14 W13) (H12 W14):(H08 W02) (H13 W05):(H04 W06) (H11 W09):(H05 W15)
(H10 W06):(H03 W09) (H14 W07):(H08 W03) (H13 W11):(H09 W10) (H04 W15):(H07 W02) (H11 W13):(H15 W08) (H06 W01):(H02 W05) (H01 W04):(H05 W14)
(H08 W04):(H07 W09) (H09 W13):(H10 W07) (H13 W03):(H11 W14) (H01 W05):(H12 W10) (H06 W15):(H05 W11) (H04 W08):(H15 W12) (H03 W06):(H14 W01)
(H04 W02):(H01 W13) (H13 W12):(H08 W05) (H10 W11):(H05 W06) (H09 W14):(H15 W01) (H06 W07):(H11 W04) (H02 W10):(H07 W15) (H14 W09):(H12 W08)
(H09 W12):(H11 W15) (H13 W01):(H05 W09) (H04 W14):(H12 W07) (H02 W06):(H15 W13) (H14 W11):(H07 W05) (H03 W04):(H01 W10) (H06 W02):(H10 W03)
(H10 W04):(H12 W05) (H11 W01):(H07 W13) (H04 W03):(H05 W08) (H03 W11):(H08 W07) (H09 W06):(H02 W14) (H13 W09):(H01 W02) (H06 W10):(H14 W12)
(H12 W06):(H05 W07) (H03 W14):(H02 W09) (H06 W12):(H15 W02) (H13 W15):(H14 W04) (H04 W01):(H08 W10) (H10 W13):(H01 W03) (H09 W05):(H07 W08)
(H13 W08):(H12 W01) (H06 W05):(H01 W15) (H14 W10):(H15 W09) (H10 W14):(H04 W11) (H03 W12):(H05 W13) (H09 W02):(H08 W06) (H11 W03):(H02 W04)
(H03 W07):(H15 W05) (H11 W10):(H12 W02) (H10 W15):(H08 W01) (H02 W08):(H05 W04) (H13 W06):(H07 W03) (H06 W09):(H04 W13) (H09 W11):(H01 W12)
(H04 W07):(H14 W15) (H05 W03):(H15 W10) (H01 W08):(H07 W06) (H03 W05):(H11 W02) (H13 W04):(H10 W12) (H02 W01):(H12 W11) (H06 W13):(H08 W14)
(H11 W08):(H01 W14) (H09 W03):(H04 W05) (H03 W13):(H12 W15) (H10 W09):(H07 W12) (H14 W02):(H05 W01) (H08 W11):(H15 W04) (H13 W10):(H02 W07)
(H05 W10):(H08 W13) (H04 W09):(H02 W11) (H03 W02):(H07 W04) (H13 W07):(H06 W08) (H09 W15):(H12 W03) (H11 W12):(H14 W06) (H10 W05):(H15 W14)
(H13 W02):(H15 W11) (H05 W12):(H07 W14) (H02 W13):(H14 W05) (H06 W03):(H12 W09) (H09 W08):(H03 W10) (H10 W01):(H11 W07) (H01 W06):(H08 W15)

Since 30 is not divisible by 4, each round must have 2 players with a bye.  You will probably want to work out who these players are, so note that they always occur in spouse pairs, for example in round 1 the pair (H5 W5) has the bye.

There are some more schedules on the message board if you follow this link.

Hope that helps,

Ian.