[Retros] "half" proof games

Noam Elkies elkies at math.harvard.edu
Fri Feb 6 14:48:00 EST 2004

NDE> There are certainly no shorter... There are other exmaples in 3,
NDE> such as 1 f3 ... 2 g4 ... 3 fxe4 ...#, and at least 4 and 5 look

Ulrich> or 1.e4 ... 2.ed5: ... 3.Ke2 and 1.d3 ... 2.Kd2 ... 3.Kc3

The first of these works; the second is cooked (1...e5 or e6;
2...Qe7 or Qh4, 3...Qb4#).

NDE> possible as well, as in 1 g3 ... 2 Bh3 ... 3 B:e6 ... 4 f4 ...#
NDE> and 1 d3 ... 2 Bd2 ... 3 Ba5 ... 4 Bxd8 ... 5 Qc1 ...#.

Ulrich> the order of Bxd8 and Qc1 is interchangeable, isn't it?

But Richard Stanley originally asked only that:

RS> *any* sequence of n White initial moves so that
RS> Black has a unique way to mate White on Black's nth move?
RS> (All n Black moves should be unique.)

There was no requirement that the *White* moves must be unique
to reach that position, or that the final position must be
a sound proof game. Note that in Richard's game White could
promote to either Rook or Queen and reach the same final position.

Joost suggests that Richard's game starting 1 g4 ... 2 g:h5 ... 3 h:g6
is cooked because Black could play either g5 or g6 on his 2nd move.
Again this is a matter of exactly which notation system is used;
in the system that uses "2...g5 3 h:g6 ep", either 3 h:g6 or 3 h:g6 ep
would have a unique solution. If the ep notation is not mandatory,
one can easily concoct some alternatives along the same lines, e.g.:

1 e4 ... 2 Q:h5 ... 3 Q:g6 ... 4 Q:f6 ... 5 Q:e5+ ... 6 Q:h8+ ...
7 Qe5+ ... 8 Qh8+ ... 9 Qe5+ ... and eventually something like
1009 Qe5+ ... 1010 d3 ... 1011 Kd2 ... 1012 Kc3 ... 1013 Q:h5 ...#

NDE