[Retros] File-filling proof games
elkies at math.harvard.edu
Sun Jan 12 01:13:54 EST 2003
In the Nov.2002 issue of The Problemist, C.Lytton concludes
his discussion of Frankiss' 11.0-mover (R322) with the curious
comment "So far no one has claimed a shorter PG to fill this file!",
referring to the f-file, which has each square occupied by a piece
in the R322 diagram. Lytton does not write explicitly that each square
must be occupied by a piece rather than a pawn, but this must be
the intention, because if pawns are allowed then there's an easy and
boring PG in only 4.0 moves, namely 1 d4 d5 2 Bf4 Bf5 3 e3 e6 4 Qf3 Qf6.
But it turns out that it takes only little more work to get a piece
on each square: simply change 4 Qf3 Qf6 to 4 Qh5 Qh4 5 Nf3 Q:f2+
6 K:f2 Nf6 7 Q:f7+ (C+ Popeye in a few seconds). I claim no artistic
interest (perhaps that was implicit in Lytton's comment...), only speed.
Indeed this SPG is fast enough to qualify as a Shorty, and it is curious
(in light of the comment on Frankiss' SPG) that the f-file the only file
for which I can do this: all other files take me 8.0 moves to fill
with pieces in a SPG, except for the d-file which takes an extra half-move
and much more work. It also takes Popeye more time (almost an hour) to solve:
Pieces White Rd1 Sd2 Bd4 Qd3 Ke1 Sg1 Rh1 Pa2 Pb2 Pc2 Pe3 Pf2 Pg2 Ph2
Black Ra8 Sb8 Bd5 Qd8 Kd7 Bd6 Sg8 Rh8 Pa7 Pb7 Pe6 Pf7 Pg7 Ph7
8 -R -S . -Q . . -S -R 8
7 -P -P . -K . -P -P -P 7
6 . . . -B -P . . . 6
5 . . . -B . . . . 5
4 . . . B . . . . 4
3 . . . Q P . . . 3
2 P P P S . P P P 2
1 . . . R K . S R 1
dia8.5 14 + 14
My 8.0-movers for the remaining files are much easier:
Popeye confirms each one in under a second, and I'm sure
the solvers on this list won't take much longer. I'll give
just one sample diagram, and list the solutions for the remaining 5.
Pieces White Ra1 Sa4 Ba7 Qa6 Ke1 Bf1 Sg1 Rh1 Pb2 Pc4 Pd3 Pe2 Pf2 Pg2 Ph2
Black Ra8 Sa5 Ba2 Qa3 Ke8 Bf8 Sg8 Rh8 Pb7 Pc5 Pd6 Pe7 Pf7 Pg7 Ph7
8 -R . . . -K -B -S -R 8
7 B -P . . -P -P -P -P 7
6 Q . . -P . . . . 6
5 -S . -P . . . . . 5
4 S . P . . . . . 4
3 -Q . . P . . . . 3
2 -B P . . P P P P 2
1 R . . . K B S R 1
dia8.0 15 + 15
B-FILE: a completely symmetrical game, in which Black mirrors each of
the White moves 1 g3 2 Bg2 3 B:b7 4 d4 5 Bd2 6 Bb4 7 d3 8 Qb3.
C-FILE: 1 d4 e5 2 Kd2 Ke7 3 Kc3 Kd6 4 d:e5++ Kc5 5 Q:d7 Nc6
6 Q:c7 Qd1 7 e3 Bd6 8 Bc4 Q:c2.
E-FILE, G-FILE, H-FILE: three more symmetrical games, with White moves
1 Nc3 2 Ne4 3 c3 4 Qb3 5 Qe6 6 b3 7 Ba3 8 B:e7,
1 b3 2 Bb2 3 B:g7 4 e4 5 Qg4 6 f3 7 Kf2 8 Kg3,
1 c3 2 Qc2 3 Q:h7 4 d3 5 Bh6 6 e3 7 Be2 8 Bh5.
I didn't spend much time constructing these, and I imagine that
shorter SPG's are possible for at least some of the eight files.
--Noam D. Elkies
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