When I am hungry

With this puzzle (#163 , #167 ) Henri Rnck won 1st prize in 1906 year.

Henri Rinck

Henri Rinck has so many puzzles and most of them are perfect - here is one of them :

White to play and win

assuming b+r+k vs b+k and r+r+b+k vs k+q are both wins then

So Kb4 would be repeating since the R can't take the B. I wonder what the actual solution is.

nswwsn and Caiello gave some of the lines and here is the  solution from the book:

This position needs some explanation : if black king can get to any of white corners of the board, the game will be a draw . Obviously author accepts it can't be done . May be somebody has different opinion ?

Bump:3

How to play black ?

Why not Bd7? It seems to avoid any mess.

Here is an evaluation and continuation of the position in post #176

There are so many variations that this is probably incorrect, but.......

Somebody to help to solve " The mystery of the 36 th move " ? :

http://www.chess.com/forum/view/help-support/play-online-against-the-computer-freezing-at-move-36

and

http://www.chess.com/forum/view/suggestions/any-solution?ncc=1#first_

About  #176 and #178 - I think like Caiello that 1...e5 is may be the best move . This was not a puzzle with exact solution, but a practical position with different possibilities. 

mate in 2 moves

Qa3+ and Qd6 mate I presume.  The rook is a little bit surplus.

Yes, you are right, thanks . I corrected the position - you can see the correction above 

1. Rh8!!

I agree.  :)  If 1...d5 or 1...d5, then 2. exd6#.  If the black rook moves off of the backrank, then 2. Nc8#.  If the black rook moves off of the f-file, then 2. Qf7# unless black plays 1...Rc8+ 2. Nxc8#.

This is very interesting...