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You have to start off with your Knight in order to free a path up for your Bishop. If you start off with your Rook, then you pretty much come to a dead end. Black has an option to capture your Knight with his pawn, but that willl only lead to a Mate in 3. After that, all of the moves are forced and Black's fate is sealed.
The following is a copy of Post #155 on Page 8 by @elindauer:
I take decisions in these puzzles exactly the way I play OTB. My goal is to find the best move with the least amount of calculation. In this case, I solved the puzzle in 3 steps:
phase 1: calculating forcing lines
- check material, see that white is winning.
- start calculating forcing lines. My first glance was Rd7+ Kb8 Rxg7. I evaluate this as winning for white but not resignable yet. This becomes my main line.
- consider other forcing checks / captures. I happened to look at Nb5+ next. First I tried Nb5+ cxb5 Rd7+. The king has a couple choices, I tried Kb8 Be5+ Ka8 and ran into a wall. I evaluate this as worse then my main line and discard it. I note that letting the king get to a8 kills my attack, and try Nb5+ cxb5 Be5+ Kc6. I look for forcing continuations, and see Rc3+, Bd7+ ... oh, Bd7+ Kc5 Bd6#... is mate! ok. So Nb5 cxb5 wins for white.
Now I looked at Nb5+ Kb8 Bd4+ Ka8 Nc7+ Kg8. I can see that Ne6+ here wins the exchange, and I already evaluate this as better than my main line. So I cut off my calculation and call this my main line.
Return to calculating forcing lines in the original position... Nd5+ cxd5 ... wait, no, Nd5+ Kb8 transposes to the main line and this is black's option. No need to calculate Nd5+ cxd5 since black will only play this if it worse for me then my main line. Ignore.
So I am ready to move. I go to the puzzle and play Nb5+ Kb8 Be5+ Ka8 Nc7+.
Phase 2: where to put the knight.
- from phase 1 I already have a main line: Ne6+ Ka8 Nxc8. I extend a little farther and see Rxc8 Bxg7 picking up another pawn too. I evaluate this as totally winning for white. In time trouble I would play this instantly. With a few minutes to spare, I calculate the alternatives:
- Na6+ Ka8 and I see nothing better then just Nc7+ repeating moves. Discard.
- Ne8+... aha this allows Rd8... Ka8 Rd8+ Bc8 Rxc8+ Kb7. I can't stop calculating just yet since the knight is pinned. However I see that Rc7+ followed by Ne6 will save the knight. Since I prefer to win the bishop then to win the exchange, and I can see that there is still some life in this line left to calculate, I evaluate this as better then Ne6+ and continue...
- Rd8+ Rxd8... Ne6+... nothing really coming to mind here. I am ready to move.
So I go to the puzzle and play Ne8+ Ka8 Rd8+ Bc8 Rxc8+ Kb7.
Phase 3: calculating the win.
Same song, different verse. I know that I have Rc7+ and just save the knight, with a winning 3 minor pieces vs a rook endgame. I calculate a few more forcing lines to see if there is a mate:
- Nd6+ is nice, only 1 answer... Ka6... Bf1+ b5... Bxb5+ cxb5 Rc6+ Ka5... seems promising but I'm not quite seeing the knockout. I put this under "consider again later" and return to other ideas
- Rb8+ Ka6 Bc8+ Kb5 I have h5+, f5+... oh wait, I see that Rb8+ Ka6 Nc7+ only allows Ka5... now Bc3+... is mate! ok I'm ready to play.
Rb8+ Ka6 Nc7+ Ka5 Bc3 winner winner chicken dinner.
So this mate in 9 can be taken over the board as three different 3 move combinations. You don't have to see the whole thing up front to solve it. Hope that helps.
seeing mate in 9 is out of my leage,so as you i first notice i am 1 move from being mated,leading me to keep oponant in check,or defend Q mate.surveying board,i have 2 check options,Rd7 or Nb5,Rd7 leads me no way to keep checking,now Nb5 puts me in an akward position,putting N in position for pxNb5,but if pxNb5 i still have checking abillity with bishop,since i opened path by moving Bd5,so its Nb5 check,surprize Kb8,new ball game,1.Nb5...Kb8,now i have B to attack with also,black king is backed up without many moves at his dispoal.2.Be5check...Ka8,3.Nc7check...Kb8,4.Ne8 makes puzzle easier,Ne8 clears path for Be5check,and blocks black R on rank 8.now my R can check with 5. Rd8...Bc8,now its down to mate in 4 instead of 9.really 3 because 6.RxBc8...Kb7,now this is within my abillity of solving the end game 7.Rb8...Ka6, 8.Nd3...Ka5, 9.Bc3#.so mate in 9 is really not as hard,if you can break it down to one move leading to another and so forth.first move is usually the hardest,and for the record i moved Rd7 first,try again,its only a puzzle,a place where mistakes can be made,hoping you learn from it
Great,if 1...cxb5 then 2.Be5+ Kc6 3.Bd7+ Kc4 4.Bd6#
ON MOVE 3.Bd7...Kc4,how does king move from c6 to c4 which takes two moves to get to c4, maybe i am wrong or someone posted on this all ready,my bad,but do you see your annalogy 1.Nd5...cxNd5,2,Be5...Kc6,3.Bd7...Kc4,4.Bd6,that move sequence is flawed,Kc6 can not get to Kc4 in one move,it might be a typo but i do not think so,recheck your moves
He meant 3...Kc5, but it is irrelevant as 3. Rc3 is checkmate. Also 1. Nd5+ only appears to work if 1...Kb8, transposing to the main line after 2. Be5+ Ka8 3. Nc7+. Otherwise it appears 1. Nd5+ ends up clogging the d-file after 1...cxd5, making it harder for the white rook to be effective, as if 2. Be5+ then the black king can go to d8 or perhaps even c6 eyeing a now free b5 square, as opposed to the 1. Nb5+ lines, although that appears risky.
Instead of 8.Nc7+ is 8.Bf1+ equally valid?
That was my first thought, but after b5 white takes a bit longer to finish the job. I think you have to play Nc7+ anyway, then Ka5 and now after Bc3, there is b4 before Bxb4# (mate in 11).
I thought the key move after spotting that Nb5+ was possible, was the discovered check 4. Ne8+ blocking the back rank cover provided by the rook on f8. After that it was just a case of finding the fast way to finish off the king hunt.
If 8. Bf1+? then 8...Rxf1+, although white is still winning easily because of the threat of Nc7+. For example after 9. Kb2 Rb1+ 10. Kxb1 Rxe8 11. Rxe8, the outcome is clear, but checkmate is delayed. If instead 9...Rf3 10. Nc7+ Ka5, white doesn't have 11. Bc3# because of 11...Rxc3, but white does have of course, 11. Rxh8, easily winning.
Oops, yes quite right I had forgotten all about rooks !!
A reminder to us all to check our analysis before committing oneself...
good but what about 6.Bxc8? threatening 7.Ba6# and 7.Bd7 and 8.Bxc6 checkmate.
6. Bxc8 allows 6...Rxe8. Any discovered checks by white allow 7...Rxd8 except for 7. Bb7+. In that case 7...Kxb7, and black appears to be winning being up a rook for a bishop with no forcing checkmate for white. If instead of 7. Bb7+ the white rook moves off of the eighth rank then 7...Rxc8 or perhaps 7...Rxe5. If 7. Rxe8 Rxe8, black's rook forks the white bishops at c8 and e5. In all of these variations black comes out ahead a rook for a bishop with no forcing checkmate for white.
6....Rxe8 7.Bd7 Rxd8 8.Bxc6#
Very nice, a quicker, yet tricky, missed two bishop checkmate for white by me. Since 6...Re8 could get black checkmated in eight moves then black could try 6...Rf1+ 7. Kb2 Rb1+ 8. Kxb1 Rxe8 9. Bd7+ Rxd8 10. Bxc6# making it longer than the puzzle checkmate in nine. Also, black can play 9...Kb7 delaying checkmate even longer as well as play 7...Kb7, in your line, delaying checkmate. Once again though, very nice checkmate! Thank you again.
Happy with this. Saw what was needed very quickly (unusually for me) in blocking black's rooks in order to bring white rook up to d8. The best way to do that is with the knight via a discovered check & then drive the king into the corner at a8. Wanted to move 1.Nb5 but couldn't see why black wouldn't take at b5 then saw the two-bishop mate. In some of these puzzles the moves seem to suggest themselves & I found it more or less plain-sailing until move 6 then undecided about taking bishop on c8 with rook or bishop ? But then you see the bishop capture doesn't work (gives black the chance to move the pawn at a7) so the rest of the moves fell into place. A good exercise in applied logic & wonderful for the morale
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