1…Kf8!, inter alia, refutes 1.Ba7?
as an attempt to mate in 2 moves.
Shortest mate?
A new motivation for mutually exclusive castlings!
A new motivation for mutually exclusive castlings!
Solution: The only possible reason why 1.Ba7? fails is
that Black can force a draw owing to the 50-move or triple-repetition rules
(first obstacle). In order to avoid Black’s defense, White needs a foreplan, so
1.h6! (this
irreversible pawn move makes it impossible for Black to refute the threat 2.Ba7
by referring to triple repetition or draw under the 50 move remis rule); but White loses a tempo and so Black can
play 1…Rgxh7. Then 2.Ba7?
is too late because 2…O-O! defends owing to the fact that castling is to be
deemed legal unless proved otherwise (secondary obstacle).Yet another foreplan
is thus needed, so: 2.O-O! and now 2…O-O?
is illegal, as the two castlings are mutually exclusive. Suppose they are both
legal. It could only be so if the move 1...Kf8! refuted the try 1.Ba7? on
account of being a 100th consecutive single move without pawn move
or capture. But in such a case, at least one position must have occurred three
times before. With both kings, the wRh1 and the bRh8 never moving (castling
rights preserved), the inevitability of a triple repetition can be proved as
follows. Let us consider the positions arising after Black’s odd retractions (1st,
3rd, 5th, etc) in the retroplay leading to the diagram
position; in all of them, the bR occupies a light-square and, since it is
impossible for either side to win or lose a tempo, the resulting position with White
to retract will be one of the following: [(bRg8/wBh7 and wRa8/wBb8 or wRa8/wBb6
or wRa7/wBa5 or wRb8/wBa7 or wRb8/wBa5) or (bRh7/wBg8 and wRa8/wBa7 or
wRa8/wBa5 or wRb8/wBb6 or wRa7/wBb8 or wRa7/wBb6)]. Since there must have been
25 positions arising after Black’s odd retractions and only 10 possible piece
permutations for them, a triple repetition would have necessarily occurred
(10x2=20<25). And so, 2…any, and now the main plan works: 3.Ba7!
any, and 4.Rxc8#.
Notice
that, firstly, the key move also results in extra guarding of the g7-square –
this is required to invalidate Black’s defense 2…Kf8/exf6! 3….exf6/Kf8!; and
secondly, White’s castling is pure of aim (only needed to rule out Black’s
castling defense.)
---------
Die Schwalbe
Heft 255 Band XXX Juni 2012, S. 527:
Lassen wir hier einmal die Autoren selbst
zu Worte kommen: (…)
Mario Richter und Ronald Schäfer kommen im
Prinzip zu der gleichen Lösung, beginnen allerdings sofort mit der Rochade als
ebenfalls die 50-Züge-Regel ausser Kraft setzendem Zug, also 1.0-0 g3 2.La7
g:h2+ 3.Kh2/K:h2 ~ 4.Tc8#. Ronald Schäfer “Eine schöne Knobelaufgabe zum
Einstieg.” Mario Richter: “Kombination aus Retrosstrategie und sich
wechselseitig ausschliessnden Rochaden. Eine ziemlich ausgefallene Komposition
zu diesem sehr speziellen Thema (mit Potential für Diskussionen)”
