# [Retros] At-home initial array challenge

Francois Labelle flab at EECS.Berkeley.EDU
Sun Mar 20 16:29:23 EST 2005

Noam Elkies wrote:

> I was lucky -- the third thing I tried worked (C+ Popeye, 11sec.):

> -Ng8, -Pe7, -Pf7 (16+13): proof game in 6.0 moves.

Congratulations! Maybe my challenge was too easy. Now I wonder if this PG
was already known to someone, or if it's another proof that finding
something is easier when you know that it exists.

> P.S. Clearly it couldn't have been in 6.5 or 7.0 moves...

I suspected that something like that was true, but was afraid to get it

(16+x) type can only be of length odd.5 or even.0
(x+16) type can only be of length even.0 or even.5

So clearly length odd.0 is impossible, but how can you dismiss length 6.5
quickly? I think that you got it wrong!

Michel Caillaud wrote:

> By the way, in 2004, Joaquim Iglesias proposed on France-Echecs a

> related puzzle that was found very hard to solve : Compose an at-home

> proof game (more than 0.0 move!) where all 16 pawns are on the board.

This is probably a nicer problem, but as you said it was already posted on

http://www.france-echecs.com/index.php?mode=showComment&art=20040821195605143

Actually that's where I got the idea to turn a problem into a composition
challenge. Too bad that the "inscriptions are suspended" on France-Echecs
for as long as I've been trying to join.

> Certainly Francois computer can confirm if Joaquim's assertion of

> uniqueness was correct?

Yes there is only one such proof game, independent of length. I discovered
this in July 2004. Actually I know every proof game with all 16 pawns on
their starting squares. The number of such problems for plies 0-24 is:

1,4,16,48,144,160,248,260,279,237,
254,253,383,435,423,335,283,186,51,85,
23,39,21,33,0

One of the maximal length examples appears as R171 in Problemesis 40.

Another challenge:

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

Francois