TL;DR

Here we take a look at a program to generate the complete schedule of tournaments with games with multiple players inside, providing an indication of need for premium ones if needed. Yay!

Not much to say, the code repository is here: tournange. It basically applies all considerations that we saw in the series of posts on tournaments.

The following sections include arrangements for 3, 4, and 5 players, as well as hints to use the program for 6 players per match. Use the program to generate the other ones, like this:

# this is valid when $n is a prime power with exponent ≥ 1
$ n=2
$ tournange "$n"
round 1:
  (*1, *2)
  (*3,  4)

round 2:
  (*1, *3)
  (*2,  4)

round 3:
  (*1,  4)
  (*2, *3)

Arrangement for 3 players

This is the arrangement for 3-players matches (9 players total, 5 premium players if needed):

round 1:
  (*1, *2, *3)
  (*5,  7,  9)
  (*4,  6,  8)

round 2:
  (*1, *4, *5)
  (*3,  7,  8)
  (*2,  6,  9)

round 3:
  (*1,  6,  7)
  (*2, *5,  8)
  (*3, *4,  9)

round 4:
  (*1,  8,  9)
  (*3, *5,  6)
  (*2, *4,  7)

Arrangement for 4 players

This is the arrangement for 4-players matches (16 players total, 7 premium players if needed):

round 1:
  ( *1,  *2,  *3,  *4)
  ( *5,   8,  11,  14)
  ( *7,  10,  13,  16)
  ( *6,   9,  12,  15)

round 2:
  ( *1,  *5,  *6,  *7)
  ( *2,   8,  12,  16)
  ( *4,  10,  11,  15)
  ( *3,   9,  13,  14)

round 3:
  ( *1,   8,   9,  10)
  ( *2,  *5,  13,  15)
  ( *4,  *7,  12,  14)
  ( *3,  *6,  11,  16)

round 4:
  ( *1,  11,  12,  13)
  ( *4,  *5,   9,  16)
  ( *3,  *7,   8,  15)
  ( *2,  *6,  10,  14)

round 5:
  ( *1,  14,  15,  16)
  ( *3,  *5,  10,  12)
  ( *2,  *7,   9,  11)
  ( *4,  *6,   8,  13)

Arrangement for 5 players

This is the arrangement for 5-players matches (25 players total, 9 premium players if needed):

round 1:
  ( *1,  *2,  *3,  *4,  *5)
  ( *9,  13,  17,  21,  25)
  ( *7,  11,  15,  19,  23)
  ( *8,  12,  16,  20,  24)
  ( *6,  10,  14,  18,  22)

round 2:
  ( *1,  *6,  *7,  *8,  *9)
  ( *5,  13,  16,  19,  22)
  ( *3,  11,  17,  18,  24)
  ( *4,  12,  14,  21,  23)
  ( *2,  10,  15,  20,  25)

round 3:
  ( *1,  10,  11,  12,  13)
  ( *2,  *9,  14,  19,  24)
  ( *4,  *7,  16,  18,  25)
  ( *3,  *8,  15,  21,  22)
  ( *5,  *6,  17,  20,  23)

round 4:
  ( *1,  14,  15,  16,  17)
  ( *4,  *9,  11,  20,  22)
  ( *5,  *7,  10,  21,  24)
  ( *2,  *8,  13,  18,  23)
  ( *3,  *6,  12,  19,  25)

round 5:
  ( *1,  18,  19,  20,  21)
  ( *3,  *9,  10,  16,  23)
  ( *2,  *7,  12,  17,  22)
  ( *5,  *8,  11,  14,  25)
  ( *4,  *6,  13,  15,  24)

round 6:
  ( *1,  22,  23,  24,  25)
  ( *5,  *9,  12,  15,  18)
  ( *3,  *7,  13,  14,  20)
  ( *4,  *8,  10,  17,  19)
  ( *2,  *6,  11,  16,  21)

Invoking for 6 players

As we saw, the 6-players matches case is trickier than the other ones, and requires taking a decision. For this reason, you must provide an additional parameter in this case:

$ tournange 6
For sixtets, please specify one of 'base', '7ok', or 'dup'

# use base, 7ok, or dup then
$ tournange 6 base
# ...

The solution is for 42 players total, playing either 7 matches (in the base case), or 8 matches (7ok or dup). The number of premium players varies depending on the case, too.

And that’s really all, folks!

This has been an interesting ride, let me know your thoughts in the comments below!

If you want to take a look at all posts, here’s the list:

ETOOBUSY 🚀 minimal blogging for the impatient

Allocating games in tournaments - a program

Arrangement for 3 players

Arrangement for 4 players

Arrangement for 5 players

Invoking for 6 players

And that’s really all, folks!