[Retros] C(64,2)

[Noam Elkies]

"Andrew Buchanan" <andrew at anselan.com> writes:

> Noam's New Year composition is beautiful.

Thanks!  The hard part (once I found the relevant combinatorial formulas)
was finding the long sequences where no tempo move can be inserted.
I couldn't quite make both phases pure "enumerative proof games"
in Richard Stanley's strict sense (where there's a unique choice of
move-set, and the question is entirely to enumerate its usable
permutations): replacing White's short sequence by b3, Bb2, Qc1
seems to work work (with Black's sequences left-right reflected), but
once wK leaves e1 there are alternative tempo losses with d1Q-e1-c1.

> I took a different approach:
>
> r1b1kb1r/pppp1ppp/8/1Nq1p2n/N2P1Qn1/8/PPP1PPPP/R1BK1B1R
>
> How many proof games in 8.5?

Neat; I figured that you'd likely construct such a pseudo-symmetrical
setting.  (Happens to be the same length as mine, but unlike mine
your problem is an SPG.)

> The last few years have been easy to represent, but 2017 promises to
> be a harder case.

Well 2017 is prime but it must be possible to reach it somehow,
even if not with twinning or symmetry features.  (My series of
New Year's greeting problems did not skip 2011.)  Plus we have
an extra day this year to think about it :-)

> Happy New Year!

Thanks,
--NDE