[Retros] All checkmate proof games up to 5.5 moves, shortest knight checkmates

[Francois Labelle]

I extended my exhaustive list of checkmate proof games to include ply 11. 
I did this because "I can", and to give some company to Hirokaz, who is 
often alone in his quest for short checkmate PGs.

Statistics about checkmates in exactly 11 plies:

number of games:  362290010907 (already known)
number of positions: 350188023
number of diagrams:  340122090
number of proof games: 2057581 (= uniquely realizable diagrams)

The number of checkmate proof games in 0..11 plies:

0, 0, 0, 0, 0, 3, 51, 1106, 3813, 47300, 216420, 2057581


APPLICATION TO SHORTEST KNIGHT CHECKMATES

Below are optimal proof games, prefixed by (#moves, #captures). I put a 
star (*) when I only improve the number of captures. I'm omitting the 
slower opposite color games.


I. Single Checkmates, by Knight itself

(5.5, 4): (Hirokaz Onoda, 2007) 6.Nxa8#
(5.0, 1): 1.f3 Nc6 2.Kf2 Nd4 3.Qe1 Nf5 4.d4 Ng3 5.Be3 Nxh1#

(4.5, 2): (Francois Labelle, 2004) 5.Nxc7#
(5.0, 3): 1.d3 c5 2.Bh6 Nxh6 3.g4 Nxg4 4.Qc1 Qa5+ 5.Kd1 Nxf2#
(5.0, 1): 1.g4 Nc6 2.Bg2 Ne5 3.Bc6 Nxg4 4.Nf3 Ne3 5.Rf1 Ng2#
(5.5, 1): 1.Nc3 e5 2.Ne4 Ke7 3.Ng5 Kf6 4.e3 Ne7 5.Qg4 Rg8 6.Nxh7#

(5.5, 1): 1.Nc3 d5 2.Nxd5 Be6 3.c3 Kd7 4.Qa4+ Kc8 5.Qc6 a5 6.Nb6#
(5.5, 4): 1.Nc3 d5 2.Nxd5 b5 3.Nxe7 Qxd2+ 4.Qxd2 Nd7 5.Qe3 Kd8 6.Nc6#
(4.0, 1): (Richard Stanley & Noam D. Elkies, 1996) 4...Nd3#
(4.5, 1): (Noam D. Elkies, 2002) 5.Nf6#
(5.5, 3): 1.Nc3 g5 2.Nd5 Bg7 3.Nxe7 Bxb2 4.Nf5 Ne7 5.Bxb2 O-O 6.Nh6#

(5.5, 0): (Hirokaz Onoda, 2007) 6.Na5#
(5.5, 0): 1.e4 e5 2.Ne2 Ke7 3.Nec3 Kd6 4.Qe2 Kc5 5.b4+ Kd4 6.Nb5#
(5.5, 0): (Hirokaz Onoda, 2007) 6.Nc5#
(5.0,*0): 1.c4 e5 2.Qa4 Bb4 3.Kd1 c5 4.Kc2 Nc6 5.Kb3 Nd4#
(4.5, 0): 1.c3 f5 2.Qb3 f4 3.Qb6 Kf7 4.Nf3 Qe8 5.Ne5#
(5.0, 0): (Hirokaz Onoda, 2007) 5...Nf4#
(5.0, 0): 1.d3 e5 2.Bh6 Qf6 3.Kd2 Qc6 4.Ke3 Nf6 5.Nd2 Ng4#
(5.5, 0): (Hirokaz Onoda, 2007) 6.Nh5#

(5.5, 0): 1.e3 d6 2.Ne2 Kd7 3.Nec3 Kc6 4.Qf3+ Kc5 5.Qd5+ Kb6 6.Na4#
(5.5, 1): 1.Nc3 d5 2.Nxd5 Bd7 3.c3 Bb5 4.Qa4 Kd7 5.Qd4 Kc6 6.Nb4#
(5.0, 0): 1.e3 d5 2.Ba6 Qd7 3.Ke2 Qg4+ 4.Kd3 Nd7 5.Nc3 Nc5#
(5.0, 0): 1.e3 c5 2.Ke2 Qa5 3.Kd3 Qa4 4.Kc3 Nf6 5.Bd3 Nd5#
(5.0, 0): 1.f3 d5 2.Kf2 Qd6 3.Ke3 Nd7 4.Kd4 Qc5+ 5.Kd3 Ne5#
(5.0, 0): 1.d3 e5 2.Bh6 Qh4 3.Kd2 Bb4+ 4.Ke3 Ne7 5.Nf3 Nf5#
(5.5, 1): 1.Nc3 d5 2.Nxd5 e6 3.Ne3 Ke7 4.d4 Kf6 5.Qd3 Be7 6.Ng4#
(4.5, 0): (Hirokaz Onoda, 2007) 5.Nh4#

(5.0, 0): (Hirokaz Onoda, 2007) 5...Na6#
(5.0, 0): (Hirokaz Onoda, 2007) 5...Nb6#
(4.5, 2): 1.e3 e6 2.Qf3 Ke7 3.Qxb7 Kd6 4.Qxc7+ Kd5 5.Nc3#
(5.5, 1): 1.c3 d5 2.Qc2 Bh3 3.Nxh3 Kd7 4.Nf4 Kd6 5.Qg6+ Ke5 6.Nd3#
(4.5, 0): (Goeran Forslund, 1996) 5.Nf3#
(4.5, 1): 1.e3 e6 2.Qg4 Ke7 3.Ne2 Kf6 4.Qxg7+ Kf5 5.Ng3#
(5.0, 0): (Hirokaz Onoda, 2007) 5...Nh6#

(5.0, 0): (Hirokaz Onoda, 2007) 5...Nd7#
(5.0, 0): (Hirokaz Onoda, 2007) 5...Ne7#

[no example to the 1st rank]

with promotion:
(5.5, 2): 1.a4 c5 2.a5 Qb6 3.axb6 Nc6 4.bxa7 Rb8 5.a8=N Nd8 6.Nc7#
(5.5, 3): 1.f4 c5 2.f5 Qc7 3.f6 Kd8 4.fxg7 Nf6 5.gxh8=N Ne8 6.Nxf7#
(5.5, 2): 1.c4 e5 2.c5 Ne7 3.c6 Rg8 4.cxb7 c5 5.bxc8=N Nbc6 6.Nd6#
(5.5, 1): 1.f4 e5 2.f5 Ba3 3.f6 Ne7 4.fxg7 Rf8 5.g8=N Na6 6.Nf6#


II. Discovered Checkmates
(but contrary to Hirokaz, no condition on the mating net)

(5.5, 3): 1.e3 d5 2.Qh5 Bh3 3.Nxh3 Nd7 4.Ng5 Rb8 5.Nxf7 g5 6.Nxh8#

[no example to the 7th rank]

(5.5, 0): 1.e3 d6 2.Qf3 Kd7 3.Qf4 Kc6 4.Ne2 Kb5 5.Nd4+ Ka4 6.Nc6#
(5.5, 2): 1.e3 d5 2.Qh5 Bh3 3.Nxh3 Nd7 4.Ng5 Rb8 5.Nxf7 g5 6.Nh6#

(5.5, 2): 1.e3 d5 2.Qh5 Bh3 3.Nxh3 Na6 4.Ng5 Rb8 5.Nxf7 g5 6.Ne5#

(5.0, 0): 1.e3 d5 2.Ke2 Qd6 3.Kf3 Nd7 4.Kg4 Qg3+ 5.Kf5 Nc5#
(5.5, 0): 1.e3 d6 2.Qe2 Kd7 3.Qa6 Ke6 4.Ne2 Kd5 5.Qa5+ Kc4 6.Nd4#
(5.0, 0): 1.e3 d5 2.Ke2 Qd6 3.Kf3 Nd7 4.Kg4 Qg3+ 5.Kf5 Ne5#
(5.0, 0): 1.e3 e6 2.Ke2 Bd6 3.Kf3 Ne7 4.Kg4 h5+ 5.Kg5 Nf5#

(5.0, 0): 1.e3 d5 2.Ke2 Qd6 3.Kf3 Nd7 4.Kg4 Qg3+ 5.Kf5 Nb6#
(5.0, 0): 1.e3 e6 2.Ke2 Bd6 3.Kf3 Ne7 4.Kg4 h5+ 5.Kg5 Nec6#
(5.0, 0): 1.e3 d5 2.Ke2 Qd6 3.Kf3 Nd7 4.Kg4 Qg3+ 5.Kf5 Ndf6#
(5.0, 0): 1.e3 e6 2.Ke2 Bd6 3.Kf3 Ne7 4.Kg4 h5+ 5.Kg5 Ng6#

(5.0, 1): 1.f3 h5 2.Kf2 Nh6 3.Kg3 h4+ 4.Kxh4 f5 5.g3 Nf7#

(5.5, 0): 1.d3 f5 2.Bf4 Kf7 3.e3 Kg6 4.Ne2 Kh5 5.g3 Kg4 6.Nc1#
(5.5, 0): 1.e4 d6 2.Ba6 Kd7 3.d3 Ke6 4.Nd2 Ke5 5.Qh5+ Kf4 6.Nf1#


III. Double Checkmates

(5.5, 4): (Hirokaz Onoda, 2007) 6.Nxa8#

(5.0,*1): 1.d3 Nf6 2.Bf4 Nd5 3.Bxc7 Nb4 4.Bd6 Qa5 5.c4 Nc2#
(5.0, 1): 1.Nf3 Nc6 2.Ne5 Nd4 3.f3 c6 4.Kf2 Qb6 5.Kg1 Nxe2#

(5.5, 0): 1.e3 d5 2.Qg4 Bf5 3.Nf3 Kd7 4.Ne5+ Kc8 5.Nd7 Bd3 6.Nb6#
(5.0,*1): 1.d4 Nf6 2.Bf4 Nd5 3.Bxc7 Nb4 4.Bd6 Qa5 5.Bc5 Nd3#
(5.0, 2): 1.g3 Nf6 2.Bh3 Nd5 3.Bxd7+ Qxd7 4.Kf1 Qc6 5.Kg2 Ne3#
(5.0, 1): (Noam D. Elkies, May 1996) 5...Nf3#
(5.5, 1): 1.Nc3 e5 2.Nd5 Bb4 3.Ne7 Bc3 4.bxc3 Kf8 5.Ba3 Qe8 6.Ng6#

(5.5, 0): (Hirokaz Onoda, 2007) 6.Nc5#
(5.5, 0): 1.c4 e6 2.Nc3 Ba3 3.b4 Qg5 4.Bb2 Ke7 5.Qb1 Kf6 6.Nd5#
(5.5, 0): 1.d3 d5 2.Bg5 Kd7 3.f4 Ke6 4.Nf3 Kf5 5.e4+ Kg4 6.Ne5#

(5.5, 0): 1.d4 f6 2.Qd3 Kf7 3.Qf3 Kg6 4.Nd2 Kg5 5.g3 g6 6.Ne4#
(5.5, 0): 1.d3 f5 2.Bg5 Kf7 3.e3 Kg6 4.Ne2 Kh5 5.h4 g6 6.Nf4#

(5.5, ?): PUZZLE!! 6.Nd3#
(5.5, 0): 1.d3 f6 2.Qd2 Kf7 3.Qb4 Kg6 4.Nd2 Kg5 5.g4 g6 6.Ndf3#
(5.5, 0): 1.d3 f5 2.Bf4 Kf7 3.e3 Kg6 4.Ne2 Kh5 5.h4 g6 6.Ng3#

[no example to the 2nd rank]

[no example to the 1st rank]


The 6.Nd3# proof game is actually the solution of a much nicer problem of 
the type "last move determines the game":

 	 "Find a game ending with 6.Nd3## (double checkmate)."

This was found by Joost de Heer and myself in 2004, and hidden somewhere 
on my webpages (mixed with other cryptic problems). I leave it as a puzzle 
if you haven't seen it before.

Enjoy,
 	Francois