LEO(LE): Chinese Queen. Moves as Queen, but captures only by hopping over a hurdle to any square beyond.
PAO(PA): Chinese piece operating along Rook lines: moves as Rook, but captures only by hopping over a hurdle to any square beyond.
VAO(VA): Chinese piece operating along Bishop lines: moves as Bishop, but captures only by hopping over a hurdle to any square beyond.
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.
Rookhopper(RH): Moves along Rook-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.
Non-stop Equihopper(NE): Moves along any line over another unit of either colour to a square situated such that the hurdle stands at the mid-point between the Equihopper’s departure and arrival squares. The English (standard) Equihopper cannot pass over an obstruction other than the hurdle when playing along Queen-lines. The non-stop/French Equihopper does not have this restriction.
Wazir(WA): (0+1) Leaper, e.g., a1 to a2; a1 to b1.
No.1239Hans Peter Rehm,
Kjell Widlert & Klaus Wenda Germany / Sweden / Austria original – 04.10.2017
White’s Pao and Vao set up threats on the thematical
squares b3,b5,d3. Black’s Leo must always place itself
between two of the hoppers on those squares so that the
two currently possible mates are guarded. After three
moves, the Leo has made a round-trip but White’s Pao+Vao
have interchanged their places so that 4.h6 can be played
with a strong threat which forces WExh6. White then
reverses his manoeuvre, interchanging his Pao+Vao again,
forcing a round-trip in the opposite direction by the Leo.
Finally, the sixth rank is opened with a sacrifice of the white
equihopper so that the Pao can mate on h6.
The interchange of places “there and back again” is called
“Lois theme” in the proofgame field, and that term could well
be used here too.
Rehm & Wenda have composed some problems with a white
equistopper (as opposed to the equihopper here), where
moving white hurdles force the black king to move around
until the white pieces have reached a better position. Two
examples are G109 and G110 in FIDE-Album 2007-09. Those
problems operate with white checks, while the equihopper
here allows the use of non-checking threats. (Authors)
A logical problem (as expected!). During the solution the NEf7 attacks two of the squares b5/b3/d3, using hurdles on two of the squares d6/d5/e5. In addition the Gd3/Gb5/RHb3 defend two of the same squares b5/b5/d3, depending on whether the bLE is on b4/c4/c3. The wPA/wVA shuffle between d6/d5/e5, changing the squares that are attacked by the NE and forcing the bLE to shuffle between b4/c4/c3. When the wLE reaches e5, 4.h6 threatens 5.PAh5#, forcing Black to play 4…WExh6. The wPA and wVA then retrace their steps, returning to the diagram position but with wPh5 missing and bWEh7 now on h6. This then allows 8.NEd5+ (yet another use for the wNE) exd5 9.PAxh6#.
The position is crowded, but fortunately all we have to do is click on each move and watch the wPA, wVA and bLE shuffle about. Things then don’t seem to be quite as complex!
The basic geometry is very pleasing, but there are several technical fairy units. The pawns on e3, f3, e2 and f2 are needed as hurdles, but they must be blocked by fairy units on e1 and f1 (do those units have any function other than to act as blocks?).
Kjell Widlert
October 18, 2017 16:20
Yes, PAf1 has another function than just blocking (which is the reason we didn’t use an orthodox rook on f1):
It stops the dual (1.PAd5 2.VAd6) 3.h6 exd5 4.NEf5 d4 5.NEb1+ PAxb1!
A logical problem (as expected!). During the solution the NEf7 attacks two of the squares b5/b3/d3, using hurdles on two of the squares d6/d5/e5. In addition the Gd3/Gb5/RHb3 defend two of the same squares b5/b5/d3, depending on whether the bLE is on b4/c4/c3. The wPA/wVA shuffle between d6/d5/e5, changing the squares that are attacked by the NE and forcing the bLE to shuffle between b4/c4/c3. When the wLE reaches e5, 4.h6 threatens 5.PAh5#, forcing Black to play 4…WExh6. The wPA and wVA then retrace their steps, returning to the diagram position but with wPh5 missing and bWEh7 now on h6. This then allows 8.NEd5+ (yet another use for the wNE) exd5 9.PAxh6#.
The position is crowded, but fortunately all we have to do is click on each move and watch the wPA, wVA and bLE shuffle about. Things then don’t seem to be quite as complex!
The basic geometry is very pleasing, but there are several technical fairy units. The pawns on e3, f3, e2 and f2 are needed as hurdles, but they must be blocked by fairy units on e1 and f1 (do those units have any function other than to act as blocks?).
Yes, PAf1 has another function than just blocking (which is the reason we didn’t use an orthodox rook on f1):
It stops the dual (1.PAd5 2.VAd6) 3.h6 exd5 4.NEf5 d4 5.NEb1+ PAxb1!