[Retros] Fastest mate? :-)

[Elkies, Noam]

Andrew buchanan <andrew at anselan.com> writes:

> Great stuff!

Thanks!  So, which of the three possibilities
is the smallest fraction of a move? :-)

> For prior art the nearest is:
> https://pdb.dieschwalbe.de/search.jsp?expression=Probid%3D%27P0004856%27

Thank you.  Mario Richter already alerted me to this one
in separate e-mail.

> However this has no retro logic, and there are
> several mates beyond the Valladao - arguably
> Noam’s non-retro representation is nicer as
> the flight square forces only the three thematic solutions.

Thanks!

> There is a typo in the second diagram, wPf5 should be on e6 I think.

Yes, that's right; good catch, and sorry if the error led
some readers on a wild goose chase.  The correct URL is thus

https://www.janko.at/Retros/d.php?ff=3Q4/3P4/2pkP3/2p1p2R/8/7B/7B/R1K5

> Would be good to see the retro logic spelled out for the first one.

I don't think there's much to do.  Black cannot have just moved:
Na5 can't come from b3 (checking Kc1); nor Pc5 from b6
(impossible bP's); nor bK from d5 or e7 (impossible double check).
But the solutions work: if 0-0-0# then Black just played Nb3a5;
if fxe6 ep# then of course Black just played e7-e5, and it's
easy to retract further (bPc5 came from d7); and if d7-d8Q#
then Black just played Ke7d6.

In another e-mail reply, François Perruchaud suggested that
in the retro setting White might be in the process of promoting on f8
(e8 would also work).  I can stop that by adding two random wP's.
Then I saw that White may also be about to complete d7xc8(e8)#;
if that's an issue then I can block these squares, for example

  https://www.janko.at/Retros/d.php?ff=2BQR3/pppP4/2PkPP2/nPp1p3/2P1P3/7P/7B/R1K5

A similar fix for the non-retro setting seems to require
obtrusive force.  But I can always argue that completing d7xc8(e8)#
can't be the solution because it's a larger fraction of a move than
completing d7-d8Q# :-)

NDE