# [Retros] Games determined by their first and last moves

Francois Labelle flab at wismuth.com
Tue Sep 17 14:34:53 EDT 2013

On 08/19/2013 01:10 PM, Noam Elkies wrote:

> Another,

> which *does* have a unique solution, starts with 1 a3 and ends

> on move 5 with White giving mate with a Rook.

I just searched for such problems up to 4.5 moves. The above is C+ by my
computer.

> Are there other such examples

> known, or discoverable by computer now that F.Labelle is active again

> (welcome back!)? There's of course 1 h4 ... 6 PxB=N#, which is unique

> even without specifying the first move;

That last claim isn't true:
1. d4 f6 2. d5 Kf7 3. d6 Kg6 4. dxe7 d6 5. Qd5 Qd7 6. exf8=N#.
Peter Rösler's problem is "6. gxf8=N#" and it cannot be strengthened to
"6. PxB=N#".

For problems of the type ?x?#, my computer found:

1. e3/e4 ... 3. QxP# (same solution as P0008139)
1. h3 ... 4... QxR# (new?)
1. h4 ... 5. RxP# (solution similar to "1. a3 ... 5. mate with a rook")

> and Labelle found a few more

> such examples (all shorter) determined completely by their last move.

> But I figure that specifying both first and last move should allow for

> a greater and hopefully even more interesting selection of puzzles.

Good idea! As you mentioned, it is possible to overspecify a problem
that is completely determined by its last move. For example my "3...
Qd4#" can be written

1. f3 ... 3... Qd4#.

It's also possible to switch colors and add a useless first move, which
for this example can give 13 problems:

1. Na3/Nh3/a3/a4/b3/b4/c3/d3/d4/f4/g3/h3/h4 ... 4. Qd5#.

Excluding these types of problems and the 4 earlier problems, I still
get a long list of problems (see below). I combine moves with a "/" when
the rest of the solution is exactly the same.

in 3.5 moves:
1. Nf3/Nh3/h4 ... 4. Bg5#
1. Nf3/f3/g4 ... 4. Qe5#
1. Nf3/f3 ... 4. Qxd5#
1. d3 ... 4. Qb5#
1. d4 ... 4. Qg4#
1. e4 ... 4. Qg4# (similar to problem above, same solution as P1254391)
1. f4 ... 4. Qf5#
1. g4 ... 4. Bh5#

in 4.0 moves:
1. d3 ... 4... d5#/Qf5#
1. f3 ... 4... Qf5# (similar to problem above)

in 4.5 moves:
1. Nc3 ... 5. c5#
1. Nc3 ... 5. g4#
1. Nf3 ... 5. Qh3#
1. b4/d4 ... 5. Qf6#
1. c3 ... 5. Nh4#
1. c4 ... 5. Qb4#
1. d3 ... 5. f5#
1. d3/d4 ... 5. Qxe8#
1. d4 ... 5. Bf3#
1. e3 ... 5. Qh3#
1. e4 ... 5. Bc3#
1. f4 ... 5. Qh4#
1. g4 ... 5. Bh3#
1. g4 ... 5. Qh3#
1. g4 ... 5. Qh4#

I should obtain problems in 5.0 moves in a few days. I'll post the
solutions in <= 4.5 moves at the same time.

François