♡ 151 ( +1 | -1 ) Man,I thought I was the first one solved it.I actually took about 20 minutes after I saw your puzzle but I was offline and it's bedtime so... Anyway,the object is clear,black has to block white's check cause white will gonna "go crazy" with the rook(white can't resist black's checkmate but he's hoping for a stalemate).1...Kg5 or h5 will lead to draw with Rg6+ or Rh6+.Kh7 also lead to draw after Rh6+ and Rh8+,now black is forced to eat the rook and it's a stalemate.So I think that black maybe will have to create somekind of environment in which black king can run and hide and white rook is to follow with only one choice.After free his way with the pawn d and f out,black king can follow the path Kh7-g8-f7-e6-d7-c8-b7-c6-d7-e8-f7-g6-h7.Noted that White rook only have one choice in each move in order to check black king,and while the king was at c6,white rook have to eat the b6 pawn and thus free the black rook for controlling the 6th row.And once the king get to h7,white's move rh6+ is denied by the Rh6# by black. Actually I think White deserve a draw for his special "mental" rook,maybe the game is draw if the black rook aern't at a6? I'm not trying to take credit from you,atrifix,since you posted it first but hope you don't mind for my puzzle explanation. By the way,I think computer will have a tough time breaking these kind of puzzles. this is a beautiful one,invincible1.
♡ 70 ( +1 | -1 ) Not terribly hard (somewhat) if you're familiar with stalemate problems; obviously Black must break the stalemate, so he either has to draw the rook to e1, h2 (all but impossible), or to h6 and play RxR. Drawing the rook to h6 is not too difficult since the pawns block most of the checks, e.g. if Black played 1... d6 2. Rxd6+ e6?? and tried to continue as in the solution then White could check along the 7th rank and grab the g-pawn, after which there is no escape. Once you figure out that Black must eventually play ...Rxh6# the rest is not too hard to work out.
Actually, computers are very good at solving these, since there is a mate at the end--however, they are incredibly bad at recognizing the draws (for example, after 2... e6).