Pretty straight-forward, as the brute force approach prevails easily:
1. Rxf6+
The attraction sacrifice 1. Rg8+ doesn’t work since, for example, 1. … Kxg8 2. Rxe7+ Kh8 3. Qxh5+ Kg8 4. Qh7 takes 4 moves instead of 3. But in a practical game, it’s also an easy, straight-forward win.
1. … exf6
1. … Qxf6 or 1. … Ke8 both lose immediately to 2. Rg8 mate.
2. Qe6
Since Black has no immediate check, White can simply spend a move to cut off the Black king’s retreat. And now there is no defense to 3. Rg8 mate.
1. Rc6
1….e6 2. Qxe6 black cannot prevent Rg8#
1….Rxc6 2. Rg8#
1. Rxf6+
1…… Qxf6 2.Rg8#
1…….exf6. 2.Qe6 No way black can prevent Rg8#
1.Rxf6+ exf6
(1…. Qxf6 2Rg8#)
(1…. Ke8 2.Rg8#)
2.Qe6 followed by 3.Rg8#
1. Rc6 e6 (1. … RxR 2. Rg8++)
2. Qxe6 Bg7 (2. … RxR++ 3. Rg8++)
3. RxR++
1.Rxf6+!
A>1…….Qxf6.2.Rg8#!
B>1…….Ke8.2.Rg8#!
C>1…….exf6.2.Qe6!!!.any move.3.Rg8#!!
First move easy to see. Second move tricky but elegant
1.R×B + PxB 2. Rg8 + Ke7 3. Qe6+++
1. Rg8+ Kxg8 (1. … Kf7 2. Ra6+ e6 3. Qxe6#)
2. Rxe7+ (Rxf6+? e6!) Kh8 (2. … Kf8 3. Qf7#)
3. Qxh5#
I had to exclude the idea of Rxf6+, either as first or second move, neither worked.
That isn’t mate in 3 because after 3. Qxh5+ 3. … Kg8
That isn’t mate in 3 because after 3. Qxh5+ 3. … Kg8
1. Rc6 e6 (1. … RxR 2. Rg8#)
2. Qxe6 Bg7 ( 2. … RxR or Rg8 3. Rg8#)
3. RxR#
1. Rc6 e6 (1. … RxR 2. Rg8#)
2. Qxe6 Bg7 ( 2. … RxR or Rg8 3. Rg8#)
3. RxR#
1. Rxf6+ exf6 2. Qe6 ~ 3. Rg8#
pht said…
1. Rg8+ Kxg8 (1. … Kf7 2. Ra6+ e6 3. Qxe6#)
2. Rxe7+ (Rxf6+? e6!) Kh8 (2. … Kf8 3. Qf7#)
3. Qxh5#
3. Qxh5 is not mate ’cause the rook g1 is scarificed
1. Rxf6 works
1. … exf6 (Qxf6, Qg8# / Ke8, Rg8#)
2. Qe6 and no defense against 3. Rg8#
Not easy. But I think I finally got it:
1.Rf6 ef
2.Qe6 …
3.Rg8#
1.Rxf6+ exf6
If 1.-Qxf6 or 1.-Ke8 then 2.Rg8++
2.Qe6! followed by 3.Rg8++
pht, 3.Qxh5+ is not mate because simply 3.-Kg8.
1. Rxf6+
1a …, Ke8, Rg8#
1b …, exf6
2. Qe6, any
3. Rg8#
Pretty straight-forward, as the brute force approach prevails easily:
1. Rxf6+
The attraction sacrifice 1. Rg8+ doesn’t work since, for example, 1. … Kxg8 2. Rxe7+ Kh8 3. Qxh5+ Kg8 4. Qh7 takes 4 moves instead of 3. But in a practical game, it’s also an easy, straight-forward win.
1. … exf6
1. … Qxf6 or 1. … Ke8 both lose immediately to 2. Rg8 mate.
2. Qe6
Since Black has no immediate check, White can simply spend a move to cut off the Black king’s retreat. And now there is no defense to 3. Rg8 mate.
1. Rxf6+ exf6 (1. … Qxf6 2. Rg8#) 2. Rg8+ Ke7 3. Nf5#