## Help for the Game of Chroma

Welcome to the network Chroma server. The challenge command is described here. Other commands are the same as for all pbmserv games.

chroma challenge [-size=n] userid1 userid2 [userid2]

Starts a new game for two or three players.

The -size option sets the board size (default 5 holes per side).

### Introduction

Chroma is a colour packing game with a simple mathematical bent, although you don't necessarily have to be simple, mathematical or bent to play it.

Rules

The game is played with 56 cubes, 14 in each of four different colours (red, green, blue and white).

`     +---+      +---+      +---+      +---+      /r\rrr\    /g\ggg\    /b\bbb\    /w\www\    +rrr+---+  +ggg+---+  +bbb+---+  +www+---+      \r/rrr/    \g/ggg/    \b/bbb/    \w/www/      +---+      +---+      +---+      +---+ .`

The cubes are arranged in repeated sequences of { R,G,R, B, ...} for the first player and { W, B, W, G, ...} for the second player, and hence played in the following order:

R, W, G, B, W, R, B, G, ...

The board is a triangular grid of triangular holes which will each snugly hold a cube placed corner-downward, sort of like a triangular egg carton for tilted cubes. The default board has five holes per side.
`      +---+     /   . \       + . .   +---+      \   . /   . \         +---+ . .   +---+      /   . \   . /   . \       + . .   +---+ . .   +---+      \   . /   . \   . /   . \         +---+ . .   +---+ . .   +---+      /   . \   . /   . \   . /   . \       + . .   +---+ . .   +---+ . .   +     \   . /   . \   . /   . \   . /      +---+ . .   +---+ . .   +---+                /   . \   . /   . \   . /    + . .   +---+ . .   +---+                      \   . /   . \   . /      +---+ . .   +---+                            /   . \   . /    + . .   +---+                                  \   . /      +---+`

Play: The board is initially empty. Players take turns adding the next cube in the sequence to the board such that it does not directly sit on top of or visibly share an edge with another cube of the same colour. Cubes may stack on three existing mutually adjacent cubes provided that all four cubes are of different colours.

Aim: The last player to move wins.

Notes

Chroma is an embodiment of the 4-colour theorem in topology.

The 56 cubes may be packed to completely fill the board such that no adjacent cubes are of the same colour (provided that there are 14 of each colour).

The maximum number of cubes required for a given board size is given by the tetrahedral number Tn = n (n + 1) (n + 2) / 6.

The phased cube ordering means that players must cycle through the three intervening colours before playing the same colour again.

Three-Player Game: Not supported at the moment.

Four-Player Game: Not supported at the moment.

Syntax

chroma move <game#> <userid> <passwd> g:d3            Play a green cube at position d3.

Test Options

The following options, mainly to do with the initial distribution of pieces, are provided for testing:

The -fixed option specifies that players with a fixed number of pieces.
The -packable option specifies that the distribution of pieces will completely pack the board.
The -nonpackable option specifies that the distribution of pieces need not necessarily completely pack the board.
The -equal option specifies that players may start with an equal number of cubes of the same colour.
The -nonequal option specifies that players may not start with an equal number of cubes of the same colour.
The -adjacent option specifies that pieces must be played adjacent to at least one existing piece.
The -nonadjacent option specifies that pieces need not be played adjacent to any existing pieces.
The -extreme option starts the game with a greater disparity in colour counts.
The -no_extreme option starts the game with a reduced disparity in colour counts.
The -sequential option specifies a fixed order {R,G,B,W} in which the colours must be played.
The -nonsequential option removes the fixed order (players maintain their own sets of pieces).
The -random option specifies that players start with a shared pool of randomly drawn pieces.
The -phased option specifies that players must place pieces in the order {R,G,B,W,B,W,R,G}.
The -asymm_a option sets sequence {R,G,R,B,W,B,R,G} for player 1 and {W,B,W,G,R,G,W,B} for player 2.
The -asymm_b option sets sequence {R,G,R,B} for player 1 and {W,B,W,G} for player 2.

History