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1 - White to play and win
vertical cylinder: one can go from the a-file to h or from h to a.
For example, in the position, the black king can go to h8, h7 but not h6 where it would be in check by the a5 pawn!
horizontal cylinder: you can go from row 8 to 1 or from 1 to 8
{a) normal chessboard}
1.a5-a6 Ka7*a6 2.b7-b8=R ! {The only move in normal play, but in cylinders, you cannot force mate with the rook.
b) vertical cylinder}
1.a5-a6 Ka7*a6 2.b7-b8=Q ! {The Black King can escape, so there is no stalemate.} Ka6-h7
{c) horizontal cylinder}
1.Kb4-b5 {(or other but not 1 a6, the only bad move in horizontal cylinder)} Ka7*b7 2.a5-a6+ Kb7-a7 3.Kb5-a5 Ka7-b8
4.Ka5-b6 Kb8-a8 5.a6-a7 Ka8-a1 6.Kb6-b7 {followed by} 7.a7-a8=Q {etc.Note that in a toric chessboard, the study would be
insoluble !}
2 - hs#2,5 kobul b) Nc5 on c4
Kobul : A King catches the moving way of the last captured piece of his side.
In the particular case of the capture of a pawn, it resumes its normal march
{}
a)
1...Sb5-d6 ! {(The key is justified by the prohibition of a final 3...Qxd4+, after which there would be Ka3!.)}
2.Qc2-a4 + Sc5*a4[c6=rQ] 3.rQc6*a4[a1=rS] + Qd8*a5[a4=K] # {
By capturing a pawn, the bQ gives back to the wK its original march. The wK cannot capture it, because the bK would become a Queen and thus it would be a
self check. And 4 Kb3 is forbidden, as Black's King always has the march of a Knight. ( pictured )}
4.rKa4*a5[a1=rQ] {)}
b) bSc5-->c4 {Nc5 --> c4}
1...Sc4-b6 ! {(to forbid a final 3...Qxa5+ after which there would be Kd3!)} 2.Qc2-c3 + Sb5*c3[c6=rQ] 3.rQc6*c3[a1=rS] + Qd8*d4[c3=K] #
{b3 & c2 are controlled by the Knight-King a1 and the Black Queen is untouchable because then ...King-Queen a1xd4(pictured}
4.rKc3*d4[a1=rQ] {)}
3 - 4# with locusts
Locust : moves along the Queen's lines with the help of a sautoir, which she swallows
and behind which she lands
Loustau, JM.2015
white Pa5b4b2e2 Sa7d2 Rc4 Ka6 Bc1b1
black Bh5 Ka4 Lg1g3g4g6 Qh2 Pg2 Rh3
Isardam : it is illegal for 2 opposing units of the same kind to observe each other.
Circe: A captured piece is reborn on its native square if it is free otherwise it disappears
Rittirsch, M.1999
white Qf4 Pd7 Kg6 Rb7
black Bf8g4 Kc6 Qa4 Pe7b4b3d2e2g2h3 Sg3 Ra6e8
{ }
a) {}
1.e2-e1=Q Qf4-d4 2.Sg3-e2 d7-d8=S #{it's mat because } 3.Re8*d8[+wSg1] {is impossible
and the same for } 3.Se2*d4[+wQd1] {}
b) bRa6-->e4 {Ra6-->e4}
1.e2-e1=R Rb7-b5 2.Bg4-e2 d7*e8=B[+bRa8] # {
here too it's mat because } 3.Ra8*e8[+wBf1] {impossible,
comme } 3.Be2*b5[+wRh1] {ou} 3.Kc6*b5[+wRh1] {AUW}
6 - 2# anti-circe with rook-lions & bishop-lions
Rook or Bishop Lion: moves as a rook or bishop, respectively, using a sautoir.
The squares must be free between the start square and the sautoir, as well as between the sautoir and the finish square
Anti-Circe: a capturing piece is reborn on its original square if it is free otherwise the capture is illegal.
Note that the black king is not in check, because b7xc8 would require either a rebirth on b1, d1, f1 or h1 in case of orthodox promotion,
or a rebirth in c8 in case of promotion in rook or bishop, because we suppose that the fairy pieces come from promotion.
But this revival is impossible in Cheylan type, which is always the case when one does not specify, notwithstanding the fact that the
notwithstanding the fact that the anti-circle was invented by F.Calvet.
Gvozdjak, P.2008
white Bd1 Ke5 Qh1 Ph2c2b7e7f6h5 Sd7e8 Rf1 RLb1
black RLb6c5d4f3 BLe1h3b8 Sd6g8 Kc8 Pf2h6f7
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