Object: Checkmate the opponent's King.
 
Variant 1: Monochromatic Chess
A piece can only move to a square of same colour.
Hence Knights cannot move at all (but they keep the opponent's King from moving onto the squares they are threatening), and castling can only be done on the King's side.
Pawns can only move forward two steps in the first move, but can capture.
 
Variant 2: Bichromatic Chess
A piece can only move to a square of different colour.
Hence Bishops cannot move at all (but they keep the opponent's King from moving onto the squares they are threatening), and castling can only be done on the Queen's side.
Pawns cannot capture.
 
Apart from this the standard chess rules apply.
 
References to Chromatic Chess can be found in several places; e.g. see Raymond Smullyan's book 'The Chess Mysteries of Sherlock Holmes'.
 
 
More freeware as well as real puzzles and games at http://karl.kiwi.gen.nz.