No.585 by Neal Turner – Three different mates by a black Royal Grasshopper in s#2 with detailed author’s comments! (JV)
Definitions:
SAT: A king is in check if any of its flight squares are unguarded by opposing pieces.
Grasshopper(G): Moves along Q-lines over another unit of either color to the square immediately beyond that unit. A capture may be made on arrival, but the hurdle is not affected.
Royal piece: Piece that executes a function of the King on the board.
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No.585 Neal Turner
Finland
original – 15.08.2014
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Solution: (click to show/hide)
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White sd2 bh3h4 pd7f3g2g7h6
Black ga3 sd8 pa6b3b4e7f7
White royal gc5
Black royal gf6
s#2 SAT (9+8)
Royal Grasshoppers: c5, f6
Grasshopper a3
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1.Sd2-c4 ! threat:
2.g2-g3 +
2...rGf6-f2 #
1...Ga3-a7
2.Sc4-d6 +
2...rGf6-c6 #
1...e7-e6
2.Sc4-e3 +
2...rGf6-d6 # {
(C+ by Popeye 4.67)}
Black's defenses result in a specific White move stopping the mate. White refutes by playing that move on his second turn.
In the threat 2..rGf2 is double-check which can't be defended.
Black's strategy is to turn it into a single check which White can then defend.
1..e6 removes the wrG's flight on f8, now White can defend the check on g1 by blocking the line with 3.Se3.
But now a new flight for the brG has appeared on d6. Removing the knight will force Black on to the square, it's check on e7 but White can block with the bishop.
So the knight must come to e3 producing a flight on f2 and now it's again double-check - on the same diagonals as in the threat but with different checking squares!
On a7 the Grasshopper neutralises the check on g1, while the new guard of e7 enables the knight to come to d6 to block the check on f8.
But White jumps to d6 immediately and the brG must run to c6.
White could defend the check on c7 with 3.Sb7, but with its move the brG has given up its guard of f8 leaving the knight pinned!
Some (myself included!) might raise an eyebrow over the arbitrary use of the Grasshopper, but it was the only sound way I could find to stop the check on g1 and simultaneously guard e7.
(Author)
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I suppose with the Animated Diagrams we have to have just the actual solution.
But sometimes we need to show more to make the idea clear:
1.Sc4! (> 2.g3+ rGf2#)
1…e6 (> 2.g3+ rGf2+ 3.Se3+) 2.Se3+! rGd6#
1…Ga7 (> 2.g3+ rGf2+ 3.Sd6+) 2.Sd6+! rGc6#
Maybe it’s a more interesting challenge for composers than for solvers.
Like Antikings, SAT is itself a complex condition for those new to it to grasp. Thanks to Neal Turner for the detailed explanation making me under this beautiful problem. Great !
sorry for the typo: “understand”