After composing this game, I tried to find the shortest possible 15-marble game. I theorized that, since each army was one row closer to the other, I might be able to reduce the number of preparatory moves by two. That is, instead of 10 "scoring" moves + 5 preparatory moves (for a 10-marble game), it would take 15 + 3 moves (for a 15-marble game). But with 15 marbles, I found only a 19-move game, before getting tired of searching. I submitted both games to Martin Gardner in January 1979, and he included them in his 1989 publication of "Penrose Tiles to Trapdoor Ciphers"; but I did not know about it until George Bell contacted me about a paper he was writing, which he presented at the 2006 "Gathering For Gardner". George wrote software that proved (1) 15 moves is the shortest possible 10-marble game, and (2) 18 moves is the shortest possible 15-marble game. George recently posted the shortest possible 10-marble transfer (by Octave Levenspiel). [Game "Chinese Checkers"] [Players "2"] [Army "10"] [Event "Demo of Shortest Possible Game"] [Site "Houston, TX"] [Date "1978-11-12"] [Red "David Michael Fabian"] [Black "David Michael Fabian"] [Result "0-1"] 1. c2-d2 h8-h6 2. d1-d3 i6-g6 3. a3-c3-e3 g9-g7-g5 4. a2-c2-e2-e4 h7-h5-f7 5. e4-f4 i9-g9-g7-e7 6. d3-c4 g6-g4-e4-e2-c2-a2 7. a4-c2-e2-e4-g4-g6-e8-e6 i8-i6-g6-g4-e4-e2-c2-a4 8. a1-a3-c3-c5 f9-h7-h5-f5-f3-d3-d1 9. c5-d5 e7-e5-c5-c3-a3-a1 10. b2-b4-d4-d6-f6-f8-h8 i7-g9-g7-e7-e5-c5-c3-a3 11. c1-e1-c3-c5-e5-e7-g7 h6-f8-f6-d6-d4-b4-b2 12. b3-b4 g8-g6-g4-e4-e2-c2 13. b1-b3-b5-d3-f3-f5 g5-e5-c5-c3-c1 14. f5-f6 f7-f5-f3-d3-b5-b3-b1 15. e6-g6-g8-i8 h9-h7-f7-f5-f3-d3-b5-b3 (0-1) Notation For 2-Player Board: --------------------A1 ------------------A2 B1 ----------------A3 B2 C1 --------------A4 B3 C2 D1 ------------A5 B4 C3 D2 E1 ----------A6 B5 C4 D3 E2 F1 --------A7 B6 C5 D4 E3 F2 G1 ------A8 B7 C6 D5 E4 F3 G2 H1 ----A9 B8 C7 D6 E5 F4 G3 H2 I1 ------B9 C8 D7 E6 F5 G4 H3 I2 --------C9 D8 E7 F6 G5 H4 I3 ----------D9 E8 F7 G6 H5 I4 ------------E9 F8 G7 H6 I5 --------------F9 G8 H7 I6 ----------------G9 H8 I7 ------------------H9 I8 --------------------I9
