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1) Rg6! +- forcing Rxf7+ 2) KxF7 (pointing to Nf6 and Rg8#) forcing Rf1+ 3) Nf6 forcing Rxf6 4) Kxf6 Kh7 5) Kf7 Kh8 forced 6) Rh6# 1-0
1. Rg6 Rxf7+2. Kxf7 Rf1+3. Nf6 Rxf6+4. Kxf6 Kh75. Kf7 Kh86. Rh6+ checkmate
1. Rg6 Rxf7+ 2. Kxf7 Rf1+ 3. Nf6 Rxf6+ 4. Rxf6 Kh7 5. Rg6/e6/d6/c6/b6/a6 Kh8 6. Rh6#
1.Rg6 Rxf7+ (1...Re8+ and 1...Rg1 don't help, 1...Rg7 is countered by 2.Rh6+ and mate, and anything else is followed by 2.Rg8#)2.Kxf7 Rf1+ (if 2...Rh1 then 3.Rg8+ Kh7 4.Nf6+ Kh6 5.Rg6#)3.Nf6 Rxf6+ (otherwise either 4.Rg8 or 4.Rh6 is mate)4.Kxf6 Kh7 5.Kf7 Kh8 6.Rh6#
I must be overlooking something here- I can mate, but in 7:1. Rh7 Kh72. Kf7!And now white is threatening Nf8 followed by Rh6. If black sacrifices at e7, he can extend the game out to seven moves total:2. .....Re73. Ke7 Kg7 (or Kg8)4. Re6 Kg8 (Kh8 5.Kf7 Kh7 6.Rf6)5. Kf6 Kh7 (Kh8 6.Kg6 Kg8 7.Re8#)6. Kf7 Kh87. Rh6#I have tried every single variation in this line, and always end up with 7 moves at a minimum.Back at 2, black can try to cover the h-file with his rook, but this is a 6 move mate total:1. Rh7 Kh72. Kf7 Rh13. Rg6! Threatens Nf6+ followed by Rg8#. Black can check from f1, but white blocks with the knight and proceeds to mate with Rg8. Black can try to sacrifice the rook at g1, but white checks from f6 with the knight and mates with Rh6. Finally, black can move the king to h8 at move 3, but white checks first from g8 with the rook, and then with the knight from f6, and mates with Rg6. All of these in 6 moves total.Either the problem is wrong, or I am overlooking something really obvious here.
1.Rg6 Rxf7+(1...Re8+ 2.Kxe8 Rxf7 3.Kxf7 Kh7 4.Nf6+ Kh8 5.Rh6#)(1...Rg7 2.Rh6+ Rh7 3.Rhxh7#)2.Kxf7 Rf1+(2...Kh7 3.Nf6+ Kh8 4.Rh6#)3.Nf6 Rxf6+(3...Rh1 4.Rg8#)4.Kxf6 Kh7 5.Kf7 Kh8 6.Rh6#
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