Originally posted by ilywrin
In that case I guess the first move is 1.Bb1.
Though it is obvious White's king should descend to a1, then the bishop should return to a2 and the king procceds through the first rank I am missing the strategical concept behind it. May it ...[text shortened]... at c2 with the king allowing for Bb1-Ba2 type of "empty" moves?
Notice that in the starting position black is in zugzwang. A king move results in mate (1. ... Ka8 2. Ka6 and 3. b7#, 1. ... Kc8 also results in checkmate however it is longer). The knight is also stuck defending the f3 pawn.
With 1. Bb1 white forces black to move a pawn as all other moves lose. Now the white king moves down the board. 2. Ka4 (All other moves lose). The white king can no longer reach a6 so black can shuffle back and forth between a8 and b7. Now it seems clear that white must reach a5 (threatening a6) when black's king is on b7 forcing a pawn move. That means white must lose a move, through triangulation. The closest place is is f1-f2-e1. So of the white king goes:
1.Bb1 h6 2. Ka4 Ka8 3.Ka3 Kb7 4.Ka2 Ka8 5.Ka1 Kb7 6.Ba2 Ka8 7.Kb1 Kb7 8.Kc1 Ka8 9.Kd1 Kb7 10.Ke1 Ka8 11.Bb1 (if 11. Kf1 then d3 -+ ) Kb7 12.Kf1 Ka8 13.Kf2 Kb7 14.Ke1 Ka8 15.Kd1 Kb7 16.Kc1 Ka8 17.Ba2 Kb7 18.Kb1 Ka8 19.Ka1 Kb7 20.Bb1 Ka8 21.Ka2 Kb7 22.Ka3 Ka8 23.Ka4 Kb7 24.Ka5
Now black cannot play Ka8 as shown before.
24. ... h4
This repeats and every 23rd move hereafter black must move a pawn eg. 47, 70, 93, 116, 139, 162, 185, 208 and 231.
After move 231 white continues as before with the long walk to triangulation. However this time when he returns black won't have a pawn to move.
Postion after 254. Ka5
The longest way to mate here is for black to play 254. Kc8 I believe. However working out the best play from here is too long a task for me to undertake (I'm lazy).