New ideas in fairy chess 6 - SAT in helpmates

1.e4 Sxd4 2.Rf5+ Sxf5#

1.d3 Be1 2.Rh4+ Bxh4#

1.c5 d8B 2.Qf6+ Bxf6#

White has to unpin 3 black pieces initially blocking bKs orthodox flights (that's why any their move in diagram position would mean selfcheck for Black). The unpinned pieces then check wK by move to its orthodox flight previously guarded by them. Finally White parries check by blocking the orthodox flights and simultaneously mates Black as black pieces cannot return (they are captured). Source : 4.10.2004

1.h6 g3 2.hxg5 Kf3#

1.g3 Sf2 2.gxf2 Kf1#

1.b4 d4 2.b5 Kd3#

1.a3 Sb2 2.axb2 Kd1#

Both kings provide each other with guarding many flights. After guarding and blocking of many wKs potential orthodox flights, however, he steps away and suddenly mates bK. Star of wK surprisingly achieved.

a) 1.Se2 Sf3 2.Bg6 Sxg5#

b) 1.Sf2 Sg3 2.Rg6 Sxh5#

The analogy of two solution is absolute if not rich. B1 unpins, in W1 wSs gallop for the mating square. Then Black uses Grimshaw to prevent recapture defence against the mate and White executes bK by well known unblocking capture.

a)
1.f4 Bf5 2.Bxf5(B) Bc2#
1.a5 Ba6 2.Rf2 Be2#

b)
1.h3 Bh4 2.Rf1 Be1#
1.a2 Ba3 2.Sd3 Bc1#


Black king is surrounded by his army. The situation in Andernach chess is a bit different from one in the normal SAT - capture on the potential orthodox flight gives nothing as capturer changes the colour immediately. This prevents unblocking by capture. However captureless move to vacant potential flight is deadly - Black cannot capture back to reblock. The 4 solutions run smoothly, White enters squares vacated by Black in every move.

1.Gxb7 cxb8G 2.Ga5+ Ge5#

1.Gd8 cxd8G 2.Ga7+ Gd5#

There is no good chance to move wR or wB guarding bK orthodox flights as Black has no piece available for unpinning. White thus turns to the other way of mating - closing own line aiming at bK orthodox flights. For that, however, he has to promote to grasshoppers. But it turns out, e.g. in the 1st solution, that after 1. ~ cxb8G 2. ~ Ge5+? Black might parry the check by 3.Ge3!!, reestablishing White guard on e2. This precises Black's second move that is in fact checking hideaway of "bad" grasshopper. The first Black moves have different motivations - 1.Gd8 provides meat for promoting pawn, while 1.Gxb7 is the only available tempo move - it maintains guard of d5.