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.
History
Chroma rules copyright Cameron Browne and Stephen Tavener © 2008.
The name “Chroma” refers to the importance of colour in the game.
The Chroma board with six holes per side is equivalent to the Foursite 3D board available from IQideas Ltd.
More details are available at the official Chroma page.
Implementation and Help file by Cameron Browne, May 2008.