# [Retros] Shortest checkmates in shortest proof games

Noam Elkies elkies at math.harvard.edu
Fri Oct 4 08:36:56 EDT 2002

> thanks for the nice improvements!

You're welcome.

> Considering the promotions the original intention

> was that the piece itself checkmates.

Okay; the f2 and h2 minima are still no more than 4.5:

1 e3 e6 2 Qg4 Ke7 3 Be2 Kf6 4 Q:e6+ Kg5 5 f4/h4# (each C+ 0.02 sec.)

Alternatively for h2:

1 h4 g5 2 hg f5 3 R:h7 Nf6 4 g:f6 a6 5 f7# (C+ 0.04 sec.)

> Promoted pawns (R):

> a2 SPG in 3,5 - RS 5/96

This must be an error, nothing can be promoted before move 4.5 ...

> c2

> f2

> h2

The 4.5 move game with h2 -> f8Q# from my previous e-mail also works
with f8R#. Likewise 1 f4 c6 2 f5 Qc7 3 f6 Kd8 4 fg f6 5 g:f8=R#.
(Both C+ in 10-20 milliseconds) and, with a bit more tinkering,
1 c4 b6 2 c5 Bb7 3 c6 Qc8 4 c:b7 c6 5 b:c8=R# (C+ in .03 sec.).

> Which other of the 16 + 32 SPGs are *sole* ones?

> I consider e.g. the SPG with white Ke1 as a good candidate.

Sorry, it isn't; one other example is

1 e4 e6 2 Be2 Ke7 3 Bg4 Kf6 4 Ke2 Kg5 5 h4+ K:g4 6 Ke3# (C+ in 110 msec.).

Rosler's 6 g:f8=N# game is famously believed to be the unique game that
ends with that move; it might also be the unique shortest h2 -> N# game.

There's another family of such tasks which require discovered or double
check. Two easy examples: Qd1/Pc2 and Qd1/Pe2 discovered check in 5.5 by

1 h4 e6 2 Rh3 Ke7 3 Re3 Kf6 4 g3 Kf5 5 Re5+ Kg4 6 e3#
1 d3 d6 2 Nd2 Kd7 3 Ndf3 Kc6 4 Bd2 Kb5 5 Rc1 Ka4 6 c4#

Both C+ in .02 seconds.

NDE