[Retros] Re: At home proof games in [at most] 7.0 moves

[Noam Elkies]

Thanks to Francois Labelle for sharing his latest findings!
The castling problems are particularly lovely.  Francois writes:


> 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?


Surely not too easy...  Most likely nobody has thought or dared
to look for such a proof game before.  Even with the hint that
the solutions involved castling, they were not entirely trivial
to find, especially the one with Black castling.  Can such a proof game
(necessarily 7.5 moves or longer) be found with *Queenside* castling?

The 4.5/5.5 move PG is neat too; pity about the transposition dual
that prevents the 4.5 move solution from being unique as well.
There's a locally unique sequence in 6.0 as well, 1 d4 Nc6 2 Qd2 N:d4
3 Qh6 Ne6 4 f4 N:f4 5 B:f4 N:h6 6 B:c1 Ng8, but it can't be unique
or Francois would have found it as a min+1.5 PG.

Concerning such PG's with unique solutions in both N and N+0.5:


>The number of such proof games in 8,...,14 plies is the following

> sequence (keep in mind that the two solutions could be similar).


Short of manually going through all 124 of these, maybe the computer
could be asked whether any of them have no moves in common between
the two solutions, or failing that which of the 124 minimize 
the number of shared moves.

NDE