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My solution is:
1. Rc8+, Rxc8
2. Nd4 (threatens 3. Nc6#)
2. …, Rc1
3. Nc6+, Rxc6
4. Kxc6 (and now there is no longer a stalemate)
4. …, Ka7
5. Kc7 and whites quickly.
Erik Fokke
Amsterdam, Netherlands
1.Rc8+ rxR 2.Na7 rc1 3.Nc6+ rxN 4.Kxr ka7 5.Kc7 wins.
1. Nd4 Rxc4
2. Nc6+ Rxc6
3. Kxc6 Ka7
4. Kc7 Ka6
5. b8(Q) and mate follows
Clearly, white taking black’s rook (with either the rook or knight) is a stalemate. So white should play:
1. Na7
Obviously, black has to move the rook as the king can’t legally move. If black moves the rook anywhere on the 3rd rank, white mates with 2. Rc8#. If black moves the rook to c1 or c2, white wins with 2. Rc8+ Rxc8 (forced) 3. bxc8(Q)#. So:
1. … Rxc4
2. Nc6+ Rxc6 (forced)
3. Kxc6 Ka7 (also forced)
4. Kc7 Ka6 (again forced)
5. b8(Q).
White then easily wins with K-Q versus K endgame.
1. Rc8+ Rxc8
2. Na7 Rc1
3. Nc6+ Rxc6+
4. Kxc6 Ka7
5. Kc7
Solved by Lenya Gristmilli
Rc8+ Nc7
1. Rc8+ Rxc8
2. Na7 followed by Nc6
White either mate (if black rook leaves the c-file), or win by promoting its pawn.
RC8+ R*C8
Na7 (If Rook moves out of C file,Its NC6++) If rook moves to any square in C rank, its NC6+, R*C6, KC6 leading …Ka7, then with white Kc6, its a passed pawn)
1.Rc8+ Rxc8
2.Na7
If rook moves along the 8th rank, then 3.Nc6 is a mate.
If rook moves along the c-file,
3.Nc6+ Rxc6
4.Kxc6 Ka7
5.Kc7 with an easy win.
Rc8 Rc8
Na7 Rc (anywhere)
Nc6+ Rc6
Kc6 etc
Really pretty
Rc8+ Rxc8
Na7 Rc1
Nc6+ Rxc6
Kxc6 and the pawn will queen
alternatively
Na7 Rc6+
Nxc6#
The stalemate threat lead me directly to Rc8 with no detours:
1. Rc8 Rc8
2. Na7
Here, I think Nd4 should work, too. The threat is Nc6 with either mate, or winning the rook, depending whether the black rook leaves the c-file or not. Black’s only check is from c6, and he can only move the rook, and no matter where he moves it, Nc6 is white’s next move:
2. …..Rc7
3. Nc6 Rc6
4. Kc6 Ka7
5. Kc7 and white will mate in three more moves by playing 6.b8Q, 7.Qb3, and 8.Qb6#.
1. Nd4 Rxc4 (to prevent 2. Nc6++)
2. Nc6+ Rxc6
3. Kc6 Ka7
4. Kc7 Ka6
5. b8(Q)
1-0
Na7 wins in all lines
not too difficult
No black rook’s pawn on the second rank. Black should win.
I think the answer is Na7, RxR, Nc6+, RxN, KxN, then black K has only one move, to a7, then W King moves to c7 and now white’s pawn will promote and white wins.
1. Rc8 rxc8
2. Nd4 r moves along c file
3. Nc6+ rxc6
4. Kxc6 Ka7
5. Kc7 Ka6
6. b8Q Ka5
7. Qb3 Ka6
8. Qb6#
1. Rc8+ Rxc8 2. Nd4 Rc1 3. Nc6+ Rxc6 4. Kxc6 Ka7 5. Kc7 and white wins
1. Rf8+ Rf8 2.Nd4 followed by 3.Nc6+ Rc6 4.Kc6 1-0.