# Tournament Algorithm for Quartets

I'm currently trying to find an algorithm to place players during a Mahjong tournament.

Here are the requirements :

• Number of players in the tournament : $n$ with $n \equiv 0 \pmod 4$
• Number of tables in the tournament : $n/4$ (4 players per table)
• A tournament has $x$ rounds (determinated by the algorithm according to $n$)
• A player must never meet another player twice

The goal is to find how many rounds I can set for $n$ players.

I found some documentation about Swiss-system tournament, and I would like to know if an equivalent exists for quartet instead of pairs.

-

## 2 Answers

Each player meets 3 players each round, and each player has $n-1$ other possible players to meet, so there can't be more than $(n-1)/3$ rounds. Whether it is actually possible to schedule as many as $(n-1)/3$ rounds, I don't know. People who organize bridge tournaments have to know about this kind of thing, and there is a lot of on it. I'd search for "bridge movements" and/or for "whist movements". Also, the "social golfer problem" is a good search term, as golfers go out in parties of 4.

-

Well this is a good start. I've already worked on a similar case for Bridge movements, but the problem is totally different, in the sens that Bridge players are always together (teams of 2), then it can be considered as a $1/1$ tournament, and not a $1/1/1/1$. Golfers's problem seems to be closer from what I'm searching for, I'll have a look. – zessx Jul 29 '12 at 13:16

You could look at the list of bridge movements under individual movements. Also at this page which has a lot of information on how to construct them.

-
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9807953238487244, "perplexity_flag": "middle"}