[Retros] Two little SPG-challenges

[Mario Richter]

Hello,

Christoph and Michel were asking what program I used for
finding cooks in some of their proposals.

Michel guessed right, I used my own program.
I wrote this program to support the study of chess problems 
of the type "Partially Defined Helpgames" (my personal terminology).
It's not another proof game solver.

Michel> I too was stunned ... not by the fact that the  
Michel> problem was cooked, but that the cook was produced so
Michel> quickly ...
Michel> Of course, with some luck, the  cooks can appear at the
Michel> begining of the resolution, but...

Sometimes the luck can be forced to some extent ...

I first searched for cooks that end with a non-capturing move.
In an At-Home-SPG this gives you already some (=partial) information
about the last two moves, and as you may have noticed, the cooks were
exactly of that structure.

On the other hand, Michel's LS-SPG in 11.5 moves (9+9)
(r1bqkb2/1p1pp2p/8/8/8/8/1P1PPP2/R1BQKB2) doesn't have such
easy to find cooks, and so my computer is working now for more 
than 100h, until now the only solution found is the intended one. 

(If somebody succeeded in solving this SPG with e.g. natch, it 
 would be interesting to know, how long the program needed
 to solve the problem.)


Btw., the "At-Home-SPG"-logic can be applied to the question
of the shortest LS-AH-SPG too.

Two cases:

(1) In the final position, a promoted piece is on the board.
    In the LS-SPG case this requires at least 6.5 moves and
    an example has been provided by Francois Perruchaud.

(2) In the final position, no promoted piece is on the board.
    Then, due to the LS-restriction, all moves of the side
    who moved last were made by one knight.
    If the length of the game is smaller than 6.5 moves, then
    this knight could have captured at most one opposite pawn
    outside his homebase, so the set of AH-positions to consider
    is rather small ...

greetings
  mario