[Retros] Tasks without end?

Noam Elkies elkies at math.harvard.edu
Mon Oct 7 11:34:48 EDT 2002

A few more discovered or double checkmates with a promoted piece:

# a2N/Ra1 in 6.5:
1 a4 c6 2 a5 Qb6 3 a:b6 Kd8 4 ba b6 5 a:b8=N Bb7! 6 R:a8 Ba6 7 N:a6#
(C+ 30 msec.)

## g2N/Rh1 in 6.5:
1 g4 d5 2 g5 Qd6 3 g6 Q:h2 4 gh Qd6 5 h:g8=N e5 6 R:h8 Be7 7 Nf6##
(C+ 1.1 sec.)

## g2N/h2Q(R) in 10.5:
1 g4 a5 2 g5 a4 3 g6 a3 4 gh ab 5 h:g8=N Rh6 6 h4 Rc6 7 h5 e6
8 h6 Qe7 9 h7 Qd6 10 h8=Q(R) Be7 11 Nf6## (both C+, 240 msec. each)

# g2B/h2Q(R) in 10.5:
1 g4 a5 2 g5 a4 3 g6 a3 4 gh ab 5 h:g8=B Rh6 6 h4 Rc6 7 h5 e6
8 h6 Qf6 9 h7 Be7 10 h8=Q(R) Kf8 11 Bh7# (both C+, 240 msec. each)

Note that the 10.5-movers show double or discovered checks
with *both* units promoted. There are seven kinds of batteries
(Q/[RBN], R/[BN], B/[RN]), each of which can give either double
or discovered checkmate. If each of these involves two promoted
pawns, and we keep track of both, we get a total of 14*8*7=784
SPG tasks. Add to that the cases where only one pawn is promoted,
and the total number of tasks comes to about a thousand. Yet another
kilotask looms when we ask for Black instead of White checkmates.
Do we really need to see proof games showing all 2000 of these
combinations? What kind of confidence could we have in any one
of those games being minimal (except for the relatively few
that can be realized in the theoretical minimum length,
as in the above two cases of 10.5)?...


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