py_20180508

{

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 !}

{

} 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] {)}

{

Tries
} 1.Bb1-c2 + ? Lg6*c2-b1 ! {
} 1.b2-b3 + ? Lg3*b3-a3 ! {
} 1.b4-b5 + ? Lg4*c4-b4 ! {
} {


} 1.Sa7-c8 ! {Does not threaten} 2.Sc8-b6 # {because of} 2...Lg1*b6-a7 {but...

} 1...Qh2-h1 {threat variant} 2.e2-e4 {threatens both} 3.b4-b5 # {and} 3.Bb1-c2 # {
} 2...Lg4*e4-d4 3.Sc8-b6 + Ld4*b6-a7 4.b4-b5 # {
} 2...Lg6*e4-d3 3.b2-b3 + Ld3*b3-a3 4.Bb1-c2 # {

} 1...Rh3-h4 2.e2-e3 {threatens both} 3.Sc8-b6 # {and} 3.b2-b3 # {
} 2...Lg1*e3-d4 3.b4-b5 + Ld4*c4-b4 4.Sc8-b6 # {
} 2...Lg3*e3-d3 3.Bb1-c2 + Ld3*c2-b1 4.b2-b3 # {

Incidentally on} 1...Lg4*e2-d1 ? {,reply is } 2.b4-b5 # {

Plachutta and organ pipes with Locusts.}

{

} 1...Sd4-b5 2.Ke5-f5 Sb5-d6[e4=w] + 3.Kf5-e5 Ke3-d3 4.Be7-g5 Sd6-f7[g5=w] # {

} 1...Ke3-d2 2.Se6-f8 Kd2-c3 3.Be7-b4[f8=w] + Kc3-c4 4.Bb4-e7 Sf8-g6[e7=w] #

{

} 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}

{

Tries :
} 1.Qh1-g1 + ? Kc8-c7 ! {
} 1.Qh1-g2 + ? RLc5*h5[bRLh5->h1] ! {
} 1.Bd1-e2 + ? RLd4*d7[bRLd7->d1] ! {
} 1.Rf1*f2[wRf2->a1] + ? RLb6*f6[bRLf6->f1] ! {

1st thematic try :
} 1.Ke5-f4 ? threat: 2.Qh1-g2 # {
} 1...RLf3-f5 2.Qh1-d5 # {
} 1...RLd4-h4 2.Bd1-e2 # {
} 1...Sd6-b5 2.Bd1-e2 # {
} 1...Sd6-c4 2.Bd1-e2 # {
} 1...Sd6-e4 2.Bd1-e2 # {
} 1...Sd6-f5 2.Rf1*f2[wRf2->a1] # {
but } 1...BLb8-e5 ! {
2nd thematic try : } 1.Ke5-d5 ? threat: 2.Bd1-e2 # {
} 1...RLb6-e6 2.Rf1*f2[wRf2->a1] # {
} 1...Sd6-b5 2.Rf1*f2[wRf2->a1] # {
} 1...Sd6-c4 2.Rf1*f2[wRf2->a1] # {
} 1...Sd6-e4 2.Rf1*f2[wRf2->a1] # {
} 1...Sd6-f5 2.Qh1-g2 # {
but } 1...RLc5-f5 ! {

Real play :
} 1.Ke5-e6 ! {threatens} 2.Rf1*f2[wRf2->a1] # {
} 1...Sd6-b5 {or elsewhere} 2.Qh1-g2 # {(and not } 2.Bd1-e2 + BLh3*d7[bBLd7->d1] {
} 1...Sd6-f5 2.Bd1-e2 # {(and not } 2.Qh1-g2 + RLc5*h5[bRLh5->h1] ! {
Cycle ABC-BCA-CAB

and finally
} 1...BLe1-h4 + 2.WRb1-e1 # {
} 1...BLb8-f4 2.Qh1-g2 #

{

} 1.Se8-g7 + Kf5-e5 2.f3-f4 + Ke5-d5 {
} 3.Ra6-a5 + Bd6-c5 4.d7-d8=Q + Re6-d6 {
} 5.Rh6-h5+ Bh7-f5 6.Qd8-g8+ Rd6-e6 {
Beginning of kamikaze sequence.
} 7.Qd3-c4+ Sb2*c4[-c4] 8.Ba4-c6 + Nd4*c6[-c6] 9.d2-d4 e4*d3 ep.[-d3]#