[Retros] At home proof games in 7.0 moves

[Francois Labelle]

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

http://www.geocities.com/anselan/CHE.html (and the Solutions link).

 	Francois