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Rb7 and easy draw for white.
Nd7 threatening the R and then Nf6 with Rxh7#
Nd7 should win this. The threat is two-fold- attacks the rook at b8 directly, and indirectly threatens Nf6 followed by Rh7#. Black doesn’t really have any option but to attack white’s rook with the knight:
1. Nd7 Nd5
Or Na6 and 2.Ra7 wins the piece since the rook still can’t move without allowing Nf6. If 1. …Ra8 2.Nf6 with an unstoppable mate of Rh7 coming. And, finally, Rg8 won’t hold since 2.Nf6 will still mate since 2. …Rg7 is met by 3.Rc8+ followed by 4.Rg8#. Continuing:
2. Rc5 and the double attacks will win the black knight.
White’s goal is to deliver mate with Rxh7.
1. Nd7 (threatening rook)
Black cannot play 1…Rf8, which allows
If 1…Rg8 then
2. Nf6 (threatening Rxh7#) Rg7
3. Rc8+ Rg8
4. Rxg8#
If not 1….Rg8, then white delivers mate with 2. Nf6 and 3. Rxh7.
Nd7 followed by Nf6 and Black cannot avoid Rxh7 mate without big loss of material.
1.Nd7 threatens both the black rook and 2.Nf6, leading to mate. White wins.
Nd7 and winning.
What about
Nd7 R moves
Nf6
or
Nd7 Nd5
Rc5
Maybe Kd7 attacking the rook and threatening Kf6 is better 5
I think Nd7 is the plan with which I would proceed. It serves a dual purpose. First it attacks the rook at b8, but it is really headed for f6, trapping the king in the corner with mate to follow on h7.
Black could try a counterattack by Nd5 which threatens the rook at c7, but also covers the f6 square blocking white’s plan to box the king in the corner.
However, if black tries this tactic, white will play Rc5 and one of black’s pieces will fall as now both the rook and knight are under attack with no way to protect each other. This is probably black’s best option as it will take white much longer to obtain the point with a Rook & Knight vs. Rook ending.
Of course, if black tries to prevent mate by walking the king out of the corner via g8 or g7 then white simply takes the rook.
Black might try to interfere with the mate at h7 by using his rook via g8 then g7, but the mate will then come through the back rank at c8 then g8.
1.Nd7 Rd8
2.Nf6 Rd1+
3.Kf2 Rd2+
4.Kg3 Rd3+
5.Kh4 Rd4+
6.g4 and no more checks except Rxg4 which just loses the rook
7.Rxh7#
1.Nd7 Rg8
2.Nf6 Rg7
3.Rc8 Rg8
4.Rxg8#
1.Nd7 Nd5
2.Rc5 Rd8
3.Rxd5 b4
4.Rd3 b3
5.Nc5
(a)5…b2
6.Rxd8+ Kg7
7.Rb8 and white will win
(b)5…Rxd3
6.Nxd3 and the pawn is stopped.
(c)5…Rb8
either rook of knight can take the pawn and it will either be R+N+2p vs. R+p or black will trade off the rooks and end up with N+2p vs. p.
White should win.
1.Nd7!! wins with 2Nf6 and 3Ra7 mating threats
1Nd7!!…easy win for White
1.Nd7! Rd8 2.Nf6 and Rxh7# is inevitable .Practically arab mate .
The idea on this one is to mate Black with the White rook on h7-square and the White knight on f6-square. Black can prevent this, but only at the cost of his knight.
1. Nd7
Obvious move threatening Black rook, and gaining time to move to f6-square.
1. .. Nd5
The only Black move that prevents the loss of the rook and stops the immediate Nf6.
2. Rc5
Now both Black pieces are attacked.
2. .. Rb7 3. Rxd5 b4 4. Nc5 Rb5
5. Rd8+ Putting a stop to all that nonsense.
5. .. Kg7 6. Nb3
Black’s b-pawn is blockaded by the knight, and White is a knight up.
1.Nd7 Ra8 2.Nf6 followed by 3.Rxh7
mate.
Kamalakanta