[Retros] Two little SPG-challenges

[Noam Elkies]

Mario writes:


> Did you find your solution B simply by trial and error, or did you

> - besides the missing Sb1 - find some clue, which helped you in

> finding the solution?


There's also the missing Bf8.  I aksed a standard question for
deletion/at-home SPG's: what was the last move?  It had to be
some piece going back home.  Why?  With three White men missing
on the Kingside, the most likely move was 7...Rh8 or 7...Rxh8,
and in the latter case the missing Sb1 has to go through f8 anyway
to get from h7 to h8 in only three moves.  So, after a few attempts
starting 1 Sc3 g5 2 Se4 Bg7 3 Sxg5 Be5 4 Sxh7 Bxh2, I tried to have
the Sb1 capture f8 en route to h8, and then the rest fell into place.

I had written:

N> ... that's not a fair comparison, because Natch is finding
N> a complete list of solutions and I can't claim to have proved
N> that there are no others.

Mario replied:


> Nor did Natch prove, that there are no shorter solutions...


True, but Natch still claims to have done a lot more than I did.
(NB the "last move?" heuristic meant I automatically ignored
shorter solutions with White making the last move -- not that
such a solution was likely anyway given the position...)


> I would wish the programmers of Natch & Co. would provide a switch,

> which forces the detection of shorter solutions.

> Is there any specific reason not to do so?


If all else fails you can ask Natch to solve the same position
in 6.5, 6.0, etc.

N> I see different paradoxical elements in the A and B solutions,
N> both of which have been featured many times in longer proof games,

[I meant White's 7th move in A and Black's Rh8 in B.]


> I did not mean that A and B share a common element.


Oh.


> [...] I call this challenge "Busy-King-SPG":



> In the final position of an SPG one king is occupying its

> original square.



> Construct an SPG (with a unique solution),

> where this king has made as many moves as possible.


There are quite a few SPG's satisfying this condition
where the K-trek is motivated by parity.  Some years ago
I composed one in which the Black King makes 15 of Black's
19 moves and goes back home to be checkmated.  If I remember
right, the record length of a King's parity trek now stands at 19.


> In the solution of Pos. B only one piece of each side

> does all the work, so I call this a "Lazy-Spectators-SPG".


Why is this paradoxical?

NDE