# [Retros] At home proof games in 7.0 moves

Francois Labelle flab at EECS.Berkeley.EDU
Fri Feb 4 16:56:31 EST 2005

My computer finished enumerating all the at-home proof games in 7.0 moves
or less. It feels strange because 7.0 is the maximum length for "Proof
Game Shorties", so now I know every at-home proof game that is eligible.

http://www.janko.at/Retros/Shorties/index.htm

The number of at-home proof games in 0,1,2,...,14 plies is the integer
sequence

1, 0, 0, 0, 0, 0, 0, 0, 10, 41, 116, 335, 1111, 2619, 6067.

for a total of 10300 (where a diagram which has 1 solution for multiple
lengths is counted multiple times).

TEMPO THEME

Some of these proof games aren't "shortest" proof games. Here are the
numbers of such proof games in 8,...,14 plies.

0, 0, 2, 17, 34, 89, 175.

All of them are non-shortest by 1 ply only, except for this one problem:

r1bqkbnr/pppppppp/8/8/8/8/PPP1P1PP/RNB1KBNR
PG in 5.5 moves (2 solutions in 4.5 moves)

Some of them happen to have exactly 1 solution in n-0.5 moves. Like
P1001141 by Gianni Donati, (8) Probleemblad 03/1999, with n=6.0. The
number of such proof games in 8,...,14 plies is the following sequence
(keep in mind that the two solutions could be similar).

0, 0, 2, 10, 21, 41, 50.

MULTIPLE SOLUTIONS

Joost de Heer is taking a look at proof games with multiple solutions, as
he did for plies 8-10.

CASTLING

The first problem with castling in the solution occurs at 7.0 moves. There
are two of them.

rnb1kbnr/pp1ppppp/8/8/8/8/PPPP1PPP/RNBQK3
rnbqk3/pppp1ppp/8/8/8/8/PPPPPPP1/RNBQKBN1

Apparently this theme has never been published before. Is it because it is
too easy to compose, too hard to compose, or too easy to solve?

EN PASSANT

No problem with en passant.

SYMMETRY

I found exactly 2 problems in 7.0 moves or less with a horizontal symmetry
and an asymmetric solution. The first one, in 6.0 moves, is P1004011 by
Joost de Heer, (2) Probleemblad (12/2001). The second one is 1.0 move
longer and appears in Problemesis 43.

LAZY SPECTATORS

The number of problems where only one white piece and one black piece do
all the work:

0, 0, 0, 0, 0, 16, 82

PROMOTIONS

The number of problems...

in 6.5 moves with exactly 1 promotion: 39
in 7.0 moves with exactly 1 promotion: 85
in 7.0 moves with exactly 2 promotions: 62

The 6.5-move problems are split as:

N: Pronkin 0, Ceriani-Frolkin 0
B: Pronkin 10, Ceriani-Frolkin 0
R: Pronkin 4, Ceriani-Frolkin 1
Q: Pronkin 24, Ceriani-Frolkin 0

The unique Ceriani-Frolkin problem in 6.5 moves is:
rnbqkbnr/1ppppppp/8/8/8/8/P1P1PPPP/RN2KBNR

The 7.0-move problems with exactly 1 promotion are split as:

N: Pronkin 0, Ceriani-Frolkin 26
B: Pronkin 19, Ceriani-Frolkin 2
R: Pronkin 7, Ceriani-Frolkin 3
Q: Pronkin 15, Ceriani-Frolkin 13

The 7.0-move problems with exactly 2 promotions are all
Pronkin/Ceriani-Frolkin pairs, and split (respectively) as:

N/N 0, N/B 0, N/R 0, N/Q 0
B/N 24, B/B 4, B/R 0, B/Q 5
R/N 6, R/B 2, R/R 0, R/Q 4
Q/N 6, Q/B 8, Q/R 0, Q/Q 3

These promotion pairs are consistent with what was known, there are no
surprises. See