Seating for card party problem
TimGolobic
We're hosting a Euchre party in a few weeks and I'm trying to create the most
balanced rotation of partners as possible. Here's the guidlines:
- 12 players, 3 tables of 4 players each
- 11 rounds
- each player plays in each round, no sitting out
The goal is for each player to be a partner with every other player only once
(that's the easy part). The hard part is that each player has every other
player as an opponent exactly twice.
I've tried for the last day and a half, but can't get everything just perfect.
I have an Excel spreadsheet available as a helper which computes occurences of
partners and opponents.
Thanks
- Tim
Richard Pavlicek
> We're hosting a Euchre party in a few weeks and I'm trying to create the most
> balanced rotation of partners as possible. Here's the guidlines:
> - 12 players, 3 tables of 4 players each
> - 11 rounds
> - each player plays in each round, no sitting out
>
> The goal is for each player to be a partner with every other player only once
> (that's the easy part). The hard part is that each player has every other
> player as an opponent exactly twice.
I tried to solve the same problem years ago, and it
can't be done. If you want a perfect movement, make it
a 13-player individual (13 rounds, everyone sits out one
round). For this and other ideal movements for games
of 2-4 tables see:
http://www.rpbridge.net/rpbr.htm#15
--
Richard Pavlicek
Alert! Don't miss my May bidding poll:
The Netherland Showdown: http://www.rpbridge.net/7w81.htm
Gordon Rainsford
The encyclopedia of bridge give the following set-up for the first
round:
T1 T2 T3
N S E W N S E W N S E W
12 1 4 5 7 1 3 9 10 2 8 6
Player 12 remains stationary throughout, and all other players follow
the player with the next lower number; ie Player 2 follows Player 1,
Player 1 follows Player 11.
--
Gordon Rainsford
LONDON UK
Gordon Rainsford
Having just copied this out of the book (I'm glad I attributed it!) I've
now noticed that there is a typo in the original.
The first player at T2 S should be 11, not 1.
Bruce Scott
> round:
>
> T1 T2 T3
> N S E W N S E W N S E W
> 12 1 4 5 7 1 3 9 10 2 8 6
>
> Player 12 remains stationary throughout, and all other players follow
> the player with the next lower number; ie Player 2 follows Player 1,
> Player 1 follows Player 11.
There is a typo in the encyclopedia. 5th Ed. says exactly what you said it
did. Player 1 can't be in two places at once, though. One of those number
1s must really be an 11. Looking at the rest of the movement, south at
table 2 should be player 11 instead of player 1.
This movement will satisfy the original poster's requirement for each player
to be partnered with every other player once. It doesn't take care of
playing every other opponent exactly twice, however. Player 12 gets this.
Player 1 and 2 don't (I didn't check any others). Player 2 will play
against some players 4 times and other players never.
TimGolobic
good thing that I also posted the message to sci.logic, because it can be done
perfectly. Try this link:
http://www.psc.edu/~burkardt/puzzles/tennis_puzzle.html
The 12-player and 16-player rotations are perfect: every partner once, every
opponent exactly twice.
The 8-player rotation not so good, some partners never, once, and twice, and
every opponent 1-3 times.
Thanks again
- Tim
Richard Pavlicek
> Thanks to those who replied about my Euchre seating problem. However, it's a
> good thing that I also posted the message to sci.logic, because it can be done
> perfectly. Try this link:
>
> http://www.psc.edu/~burkardt/puzzles/tennis_puzzle.html
>
> The 12-player and 16-player rotations are perfect: every partner once, every
> opponent exactly twice.
Yes, two conditions are easily arranged, but for a "perfect"
duplicate movement there are four. Each player must:
1. Partner each other person once
2. Oppose each other person twice
3. Play the same boards
4. Have the same number of comparisons (boards played in
the same direction) with each other person
The "tennis puzzle" satisfies 1 and 2. The standard duplicate
individual movement satisfies 1 and 3.
Note that you could satisfy 1, 2 and 3 by following the tennis
rotation and relaying boards each round (or using preduplicated
boards). Alas, you will find that condition 4 is way off.
TimGolobic
Solution for 8 players
8 players
(12 34) (56 78)
(13 57) (24 68)
(14 58) (23 67)
(15 26) (37 48)
(16 38) (25 47)
(17 46) (28 35)
(18 27) (36 45)
courtesy of
http://www.math.niu.edu/~rusin/known-math/93_back/whist