[Retros] "Great minds think alike"

[Elkies, Noam]

Dear fellow retro-fans,

This is the 15th year that I have been constructing
New Year's greetings of this kind:

https://www.janko.at/Retros/d.php?ff=rnbqkb1r/p2ppppp/7B/8/2B3Q1/1n2pN2/PP1N1PPP/R5RK

SPG-10.5; how many solutions?  (C+)
NDE 11.xii.2018, v. Andrew Buchanan 25.xii.2018

For the past few years Andrew Buchanan has joined me in this little niche
of our sub-subculture, constructing enumerative problems that mark
the current year (possibly in other calendars) or other occasions such as
his year of birth.  This year it turns out we composed essentially
the same problem!

The above position is a natural development of my greeting from a year ago:
https://www.janko.at/Retros/d.php?ff=1r3bnr/pppnkppp/q1b1p3/1B6/8/1P1p/P1PBNPPP/N1RQK1R1
(SPG-11.0; how many solutions?).  In January I tried to apply this
"natural development" to 2018, and concluded that it was difficult
but the arithmetic would be more cooperative for 2019; I picked up
this thread a few weeks ago, and sent out the original version
(in 10.0, without the mating move and with Qg4 instead of Qh5)
in an e-mail to a few friends who I thought might like such things.
Unknown to me, one of them knows Andrew and knows of our shared
interests in chess and mathematics, so sent it on to him.
It turns out that Andrew had the same idea in January, and
had already realized it then -- using essentially the same mechanism,
with the identical introduction.  In subsequent e-mail Andrew suggests
the above one-ply extension of my problem (which provides a "happy
ending" as he described it) though it still leaves several "loose
ends"
in the subsequences of moves; and extended his problem by 3 plies
as follows, tying together some of _its_ subsequences:

https://www.janko.at/Retros/d.php?ff=rnbqkb1r/pppp1p1p/7B/1B6/2P2P2/2N1pR1R/PP2QnP1/2K5

SPG-11.5; how many solutions?  (C+)
Andrew Buchanan, January 2018, v. 25.xii.2018

He also agreed with my suggestion of sending both positions in
the same e-mail to the retros list; so here they are.

Andrew also noted that my setting (without the mating move)
has one fewer capture but his has no obvious pawn captures.
If I try moving my Pe7 to c7 to incorporate that feature
then there are cooks -- which can be removed by changing
Black's last Knight move to a capture . . .

In my original position
(https://www.janko.at/Retros/d.php?ff=rnbqkb1r/p2ppppp/7B/8/2B3Q1/1n2pN2/PP1N1PPP/R5RK)
White can also continue 11 Nf1.  I would really have liked to
put the Nb3 on d3 and finish with Nxf2#, combining all three threads
_and_ giving a "happy ending"; alas I'm 15 years too late for this:
there are no new solutions, but 15 of the existing solutions become
illegal! So I'm left to offer it as a very late New Year's greeting
for 2004 . . .

Happy New Year,
--Noam D. Elkies