Definitions: (click to show/hide)
Vertical cylinder: A chessboard where it is supposed that the files a and h are in contact. To the right of h8 lies a8. From h8 up there is nothing.
Horizontal cylinder: A chessboard where it is supposed that the rows 1 and 8 are in contact. From h8 up lies h1. There is nothing to the right of h8.
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.
Lion(LI): Moves along Queen lines over another unit of either color to any square beyond that unit. A capture may be made on arrival, but the hurdle is not affected.
Anti-Circe: After a capture the capturing piece (Ks included) must immediately be removed to its game array square (necessarily vacant, else the capture is illegal). Captures on the rebirth square are allowed. R, B & S go to the square of the same colour as the capture; Ps stay on the file of capture; fairy pieces go to the promotion square of the file of capture.
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No.1068 Ladislav Packa
Slovakia
original – 14.05.2016
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Solutions: (click to show/hide)
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white Gg1 LIg6 Kc1
black Kc7 Sb5
h#2 (3+2)
a) vertical cylinder
b) horizontal cylinder
Grasshopper g1
Lion g6
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a)
1.Kc7-c8 Gg1-g7 2.Sb5-c7 LIg6-g8#
b)
1.Kc7-b6 Gg1-b1 2.Kb6-a5 LIg6-a8# {
(C+ by WinChloe 3.29; Popeye doesn't support cylinders)}
{ }
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No.1069 Ladislav Packa
Slovakia
original – 14.05.2016
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Solution: (click to show/hide)
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white Bd1d6 Kf7 Sc6d7 Pd2c3c4f3
black Kd3 Sa4 Bg7
#2 (9+3)
Anti-Circe
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1.Bd6-f8 ? threat:
2.Sd7-e5 # { A}
1...Bg7-e5 ! { a}
1.Bd6-b8 ? threat:
2.Sd7-c5 # { B}
1...Sa4-c5 ! { b}
1...Bg7*c3[bBc3->f8]
2.Sd7-e5 #
1...Bg7-d4
2.Sc6-b4 #
1...Bg7-f8
2.Sd7-e5 #
1.Bd6-e5 ? threat:
2.Sc6-b4 #
1...Bg7*e5[bBe5->f8] { a}
2.Sd7-e5 # { A}
1...Bg7-f8 !
1.Bd6-c5 ! threat:
2.Sc6-b4 #
1...Sa4*c5[bSc5->b8] { b}
2.Sd7-c5 # { B
(C+ by Popeye 4.73)}
{
}
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No.1068,1069 
Funny… the Lion attacks the King using the King itself as hurdle! Of course this is a speciality of cylinder boards I think.
What about a Rose-Lion on a normal board?
The principle in question is not about the board but about a “null-move”.
Can a Rose arrive to the square it occupies already or can a Rose-Lion serve as a hurdle to itself?
I think the null-move is in such positions unacceptable. Hurdle should be the thing that “stands firmly on the ground”, but rose-lion is during the move “flying in the air”. Another question is whether the king stands in the position bKc3 – wRNe8 (RN e8) in check. I think so, that it is using the same principles as in the published problem.
But Popeye does not know it …
Popeye seems to make at most one circle for rose-shaped pieces, therefore moves with longer logic are not considered.