Perspectives 
by Burt Hochberg

It's the Thought That Counts

I've never been able to muster much interest in orthodox direct-
mate chess problems. Those cluttered, unrealistic positions make
my eyes glaze over, and such terms as Nowotny interference,
Dombrovkis theme, Bristol clearance, dual avoidance, Babson
task, Indian theme, and so many others make me feel that there's a
very interesting party going on to which I was not invited.
Remarking on modern problems, David Hooper and Kenneth
Whyld, in "The Oxford Encyclopedia of Chess" (1992), observe
that "the development of obscure jargon [is] a barrier between the
composer and many solvers." My sentiments exactly.

But *unorthodox* chess problems--that's a whole nother smoke, as
an old TV commercial used to say. Way back in the 1970s, I briefly
conducted a column of humorous chess problems in "Chess Life."
It wasn't very good, but it opened my eyes to a fascinating world I
had known little about. Attracted at first by joke and trick
problems, I soon developed an interest in retractors and retrograde
analysis and then in chess variants. When an editor at Sterling
Publishing asked me to write a chess book, I suggested an
anthology of funny, unorthodox, unfair, illegal, and outrageous
problems. He agreed, and I started collecting them in earnest. (The
book, which does not yet have a title, will be published next
spring.)

My research turned up an amazing quantity of excellent material in
a surprisingly broad range of categories. In addition to problems in
grid chess, losing chess, cylinder chess, refusal chess, and other
more-or-less unorthodox variants, I found unbelievable
underpromotions, illegal castling, and a host of weird
interpretations of the laws of chess. There is clearly no limit to the
creative imagination of chess composers.

Chess creativity finds its perfect form, in my opinion, in problems
that involve retrograde analysis, such as retractors. This explains
why retrograde analysis and retractor problems have become such
popular categories of chess composition. These are puzzles in logic
superimposed on the laws and materials of chess. To solve them
you can't just assume that, for instance, castling or en passant is
possible; you have to prove or disprove it. You have to determine
the history of the position by rigorous logic.

Before I show you a couple of examples, I have to explain the
problem convention that applies to castling and en passant
captures. Castling is always permitted unless it can be proved
illegal (i.e., by demonstrating that the king or rook has previously
moved). Capturing en passant is *not* permitted, however, unless
it can be proved that the previous move must have been a two-
square pawn advance on an adjacent file.

The following beautiful retractor is one of my all-time favorite
chess compositions. Even if you don't try to solve it, you should
enjoy just following the solution.

R. Kofman, "Shakhmatniy Biulletin" 1958 (amended)

Diagram

White: Kc1, Rd1, Rd3; pawns - b4, c2, d2, f2, f6, g2, a3 
Black: Ke8, Rh8; pawns - a6, b7, c3, c7, e6, f7, g3, h6

White retracts his last move, then mates in 3

White clearly hopes to deliver mate on the last rank after, say,
dxc3. If Black castles, though, White will have no hope of mating
him anytime soon. Is there any way White can prove that Black
does not have the right to castle? (Remember, castling is allowed
unless proved illegal.)

Here's how he does it. White retracts 0-0-0, thereby proving that he
himself previously had the right to castle (otherwise he couldn't
retract it). But the fact that White had the right to castle means that
his king never left e1. If that's the case, how did his king rook get
out? Well, it didn't! The rook must have been captured on h1 (or on
g1 or f1). But how then can the rook on d3 be explained? The only
explanation is that it's a promoted pawn! White has seven pawns
on the board, so the rook on d3 is, or was, the eighth pawn.

Where could it have been promoted? If the promotion square were
somewhere on the queenside, the Black king at some point could
not have been on e8, else the new rook could not have escaped. If
the promotion were on e8 or f8, then again the Black king could
not have been on e8 at the time. If the promotion were on h8, then
the Black rook had to have moved at some point. All these cases
involve a move by Black's king or rook, prevented him from
castling.

That leaves g8. A promotion there might have occurred without
infringing Black's right to castle, since there could have been a
piece on f8 temporarily shielding the king from the new rook,
which could have escaped via the g-file. Only two pawns could
have reached g8the b-pawn or the e-pawn (the a-pawn couldn't get
to g8 without passing through f7, where a black pawn stands; this
means that the pawn now on b4 was once the a-pawn). The b-pawn
would have had to make five captures to get to g8. The pawn now
on f6 would therefore be the e-pawn, which would have needed
one capture to get there. That's six captures. The a-pawn made one
capture to get to b4. In this scenario, a total of seven captures are
needed.

Now consider the e-pawn. For the e-pawn to have promoted on g8,
it would have had to make two captures. In that case the pawn now
on f6 would be the b-pawn, which would have needed four
captures to get there. Adding the one capture needed by the a-pawn
to get to b4, we again have a total of seven captures.

But with ten of Black's original sixteen pieces still on the board,
White could not have made seven captures. Therefore the
promotion did not take place on g8 but someplace else. This means
that Black's king or rook has previously moved and proves that the
rook on d3, at some point in its history, deprived Black of the right
to castle.

Now for the brilliant solution: White retracts the move 0-0-0 and
plays 1 0-0-0! Black, having been denied the right to castle, has no
defense against 2 dxc3 and 3 Rd8 mate (1... cxd2+ 2 Rxd2, etc.).

Here's another of my favorites. This one really strains the
application of the convention regarding castling and en passant.

W. Langstaff, "Chess Amateur" 1922

White: Kf5, Rd5, Bf6; pawns - h5, h6 
Black: Ke8, Rh8; pawn - g5

White mates in 2

Let's say White plays 1 Ke6, threatening 1 Rd8 mate. Black castles
and White has no mate. But by castling Black proves that his last
move must have been g7-g5. If White knows that Black's last move
was g7-g5 giving him the right to castle, then he doesn't bother
playing 1 Ke6 and instead mates in two starting with 1 hxg6 ep

Just a minute, says Black. You can't prove that my last move was
g7-g5. It could have been Rh7-h8. If I didn't just play g7-g5, you
can't play hxg6 ep. Have it your way, says White. If you just played
Rh7-h8, that means you can't castle, so I play 1 Ke6. But in that
case, says Black, you can't prove my last move was Rh7-h8, and in
answer to your 1 Ke6 I play 1...0-0.

Round and round she goes, and where she stops nobody knows.

But what was *really* Black's last move? If this is a position with
a history, it could only have had a single history, and Black should
not be able to choose what his last move was. This is not a game,
however, but a problem, an exercise in chess logic. The position's
history does not exist in actuality but only as a logical construct.

Sam Loyd once commented, no doubt facetiously"Every composer
knows that in making a problem the pieces are not *moved* into
position, they are merely *placed*, and there has been no
*previous* play." If that were really the case, of course, the
retractor problem and all the wondrous treasures of retrograde
analysis would not exist. 