Here is a list of  solitaire (or single player) chess variants and puzzles.

• Wikipedia:
• Single player chess variants
• Chess puzzles
• Mathematical chess problems
• Chess variants pages: Problems Puzzles and Solitaire Games
• Mayhematics  site: Chess Puzzles

Zillions-of-Games scripts:

• Fifteen puzzle with chess pieces:
• Placements
• 16Plus
• Independence problem: Maximal Squadron
• Capture all pieces: Captour
• Turn all white pieces into black pieces: Chess-Maze