A few days ago
DannyJ ‘n’ AlexBear

How do I create a practice roster? 12 players, 2 at a time, 6 different pairs practice each day?

Each player needs to play with all other 11 teammates. So there will be 6 2-player teams today, and a different 6 2-player teams tomorrow, etc until each player has played with all 11 of her teammates. I know the number of combinations is 66, but how do I actually make a roster with all the different practice teams for each day?

Top 3 Answers
A few days ago
Doubly Doo

Favorite Answer

Essentially, you have the mathematical problem of arrangements (a subcategory of probability). Each player only plays with each other player once in the rotation. Using letters to represent each player we see that player A plays with B,C, D, E, F, G, H, J, K, L, and M once each or 11 times. (I skipped the letter “I” as it looks too much like J and L and can get confusing.) Because B has already been schedule to play with A (AB) or (BA) B has 10 NEW players that he faces.

The formula is 11+10+9+8+7+6+5+4+3+2+1 =66

Player M (the 12th player) has no new partners as he has been the partner for each of the other 11 players.

I went ahead and set up the grid for you and tried to explain the patterns. (This much easier to explain in person). Also, this website decided to left align the page so I had to make some adjustments from the word doc I did this on.

I have added in some XX’s into the grid as placemarkers so that the schedule lines up for you. Do this on a grid and it will all make sense (I hope.) Number 12 (xx) in each row is unnecessary it is only here to help you align the rows. Row E should have EF on day 9.

Note:I have written the letter name of the player at the beginning of each row and then stated the day they play next to it with the xx placeholders to help you out. Make a grid 13×13 fill in the info including the title, practice #s, player names (letters A-M w/o “I”) and extra xx placemarkers in last box of each row.

Player/date 1 2 3 4 5 6 7 8 9 10 11

A AB AC AD AE AF AG AH AJ AK AL AM xx

B xx xx BC BD BE BF BG BH BJ BK BL xx

C CL xx xx xx CD CE CF CG CH CJ CK xx

D DK DL xx xx xx xx DE DF DG DH DJ xx

E xx xx xx EF EG EH

EF EG EH xx xx xx

F FH FJ FK FL xx xx xx xx xx xx xx FG

G xx GH GJ GK GL xx xx xx xx xx xx xx

H xx xx xx HJ HK HL xx xx xx xx xx xx

J xx xx xx xx xx JK JL xx xx xx xx xx

K xx xx xx xx xx xx xx KL xx xx xx xx

L xx xx xx xx xx xx xx xx xx xx xx xx

M MG MB MH MC MJ MD MK ME ML MF MA xx

Player M is the 12th player in an 11 day rotation (which is why you were struggling with this so much). Her/his schedule is the balance of all the other players’ rotations so whichever letter is not represented above becomes the person who plays with M. (Note that on day 11, she plays against A and this is stated twice). [If this site accepted attachments this would have been a lot easier for both of us.]

The pattern is A with each player on days 1 (AB)-11(AM).

Player B begins on day 3 with player C (BC)[because B played with A on the first day and C played with A on the second day] and follows the schedule to day 11 (BL).

Each player after that starts two days later with C beginning on day 5 (CD) and continuing to day 1.

Player M actually has a pattern too although it is not as easy to see. Player M begins rotation on the 11 day with A, and plays every other day in alphabetical order. Day 2=B, Day 4=C, Day 6=D, and so forth. From day 10 to Day 1, 3, 5,7,and finally 9.

Player L appears to be without a partner as well but that is because his match up with M is on M’s schedule.

I recommend you keep a version of the schedule like this for the six team line up in case a person is replaced during the year and so that you have it as a guide for next year. Then consider writing each player their own schedule so they know who they face each day.

Best of luck with your team.

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A few days ago
hayharbr
Get some graph paper and write the numbers 1 – 12 across, and down, so that you have a 144 little-square block. Put x’s where 1 meets 1, 2 meets 2, etc. as well as where any number meets a number lower than itself.

Then start making your matches and put x’s where each match is. Start with 1-2, 3-4, 5-6, 7-8, 9-10, 11-12

Then start each following day with 1-3, 1-4, 1-5, up to 1-11 and fill in the others so as not to leave anyone out or give anyone two matches in one day. That should work.

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A few days ago
♥thtsjstdcky♥
try making a chart like this:

. 1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

and assign each person a number and cross off the box when two people play together…for example, if player 2 and player 6 play together, cross off the box where 2 and 6 meet

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