# [Retros] At-home initial array challenge

Mario Richter mri_two at t-online.de
Tue Mar 22 18:45:35 EST 2005

Francois Labelle> Another challenge:

>

> Find the unique (10+15) at-home proof game in 7.0 moves.

The missing black piece is the pawn d7.

I find it interesting that only one SPG for the (10+15)-case exists.

Btw. Francois, in an earlier post you made the following comments
about my suggestion for an algorithm for solving the question about
the total number of all at-home SPGs:

Francois> The version I have in mind would start with

Francois> UNSOLVED = {set of all 2^30 at home diagrams};

Francois> and then for each ply count it would try to solve everything
Francois> in UNSOLVED and move the diagrams as you're doing.
Francois> Am I missing an improvement?

I simply tried to save some seconds by not even trying to solve
those positions at ply N, which definitively cannot have a solution
at ply N (e.g. too much missing pieces. Or use your favourite
proof game solving program to check the following problem:
rnbqkbnr/pppppppp/8/8/8/8/PPPP1PPP/RNB1KBNR, PG in 9.0 - how long
do you have to wait to get the answer "No solution"?).

mario>> I have the impression that the "backward" approach might be more
mario>> suitable for answering the "All-AH-SPG"-question. What do you think?

Francois> I prefer my forward approach to enumeration. With a good pruning
Francois> heuristic, it's equivalent to the backward search of every
Francois> possible at-home problem at the same time.

Yes, but while my algorithm requires a constant amount of memory
independent of ply count, the memory requirements of your algorithm
seem to increase with the number of plies - or am I missing something?

Francois> I also find it more satisfying. I find it a little dirty
Francois> to compose problems by trying diagrams one by one. :)
Francois> But of course only the result matters.

I didn't try to construct - let alone "compose" - anything. So I think
the attribute "dirty" isn't really justified here.

greetings
mario

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