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what about
1. Rxe6 Kxe6
2. g7 Rg8
3. Kf4
white will sacrafise both pawns for the rook, takes the e-pawn and will win with his f-pawn…
1. g7 Rg8 2. R:e6 K:e6 3. Kf4 Kf7 4. h7 wins.
1. g7 N:g7 2. hg Rg8 3. Ra7 also wins, but more slowly.
1.Rxe6 Kxe6
2.g7 Rg8
3.Kf4 Kf7
4.h7 Kxg7
5.hxg8Q+ Kxg8
6.Kxe4 1-0
1. Rxe6 Kxe6 (black forced)
2. g7 Rg8 (black forced)
3. Kf4 (threatening 4. h7 Rxg7 5. h8=Q) Kf7
4. h7! Kxg7 (forced to avoid white’s promotion after Rxg7)
5. hxg8=(Q/R)+ Kxg8
6. Kxe4 Kf7
7. Kf5 with oposition – white wins
Another possibility is:
6. Kxe4 Kg7
7. Kf5 Kf7
8. f4 with oposition – white wins
It is tempting to try the sacrifice at e6, but the black king is just too close to the pawns for this to work for either a win or a draw for white:
1. Re6 Ke6
2. g7
Here, h7 is no better since black just plays Kf6 and the g-pawn falls immediately while the rook continues to cover h8. Continuing:
2. …..Rf3!
This is the only move for black, but it is enough to win. Continuing:
3. Kg2 Kf7 (white in zugzwang now)
4. Kg1 Rh3 and both pawns will fall while white will not even be able to win the black e-pawn.
So, white must try something else. Playing 1.h7 or playing g7 need to be looked at:
1. h7
Here, if he wants to retain the advantage, black will have to move the knight. There are only two squares for it- f4 and g7. On Ng5, white will win with 2.g7 attacking the rook and forcing black to take at h7 with the knight netting the rook for the two pawns, leaving white with a rook vs knight in a pawn endgame. Knight moves of 1. ….Nd8/c5/d4 are even worse after 2.g7. Let’s look at both of the suggested moves of Ng7 and Nf4:
1. …..Ng7
2. Kh4
The idea for this is that I would like to take h5 away from the knight and threaten Kh5 if the knight moves from g7, but I don’t think it makes a lot of difference what white does here since black can always just move the rook along the 8th rank when he needs a move. Continuing:
2. …..Rh8 and this is almost certainly a draw- black must defend h8 with the rook, and the knight is pretty much stuck at g7 since Ne6 will lose to Re6, and Ne8 will lose to Kh5.
At move 1, black might do just a little better with Nf4, but I still don’t see a way forward for either player:
1. h7 Nf4
2. g7
Is there anything better for white here? If so, I don’t see it. Continuing:
2. …..Nh5 (only move, of course)
3. Kg2 Ng7
4. Ra7 Kf6
5. Ra6 Ne6
6. Kg3 Rh8
7. Ra7 Kg6
8. Kg4 Rh7 (any better?)
9. Rh7 Kh7
10.Kf5 Nc5 (else lose the pawn)
11.Ke5 Kg6 (else lose the pawn)
12.Kd5 Kf5 (else lose the pawn)
13.Kc5 Kg4 (Kf4 no better)
14.Kd4 Kf3
15.Kd5 and neither player can make progress- any attempt by black to take at f2 loses the last pawn, and the white king must remain in contact with the e-pawn to keep black from winning at f2.
In my next comment, I will look at the other first move alternatives for white.
1.Rxe6 ?? Kxe6 2.g7 Rf3+ and 3….Kf7! -+
but 1.g7! Rg8 (Rb8 for instance 2.Rxe6 Kxe6 3.h7 Kf7 4.h8/Q +-) 2.Rxe6 Kxe6 3.Kf4 Kf7 4.h7 +-
so 1….Nxg7 2.hxg7 and the rook ending is most probably won +-
My first guess 1.Rxe6! Kxe6 2.h7! (not 2.g7 Rf3+) followed by 3.g7.
White should win this starting with RXN fi=ollowed by g7 This will lead to a K vs K + P ending where white wins by gaining distant opposition.
In my first comment, I discussed both 1.Re6 and 1.h7 as first moves for white. 1.Re6 is a clear loss for white, while 1.h7 is a draw for white at best. Let’s continue with 1.g7:
1. g7
It is easy to see this is better than the previous two moves I discussed. On any rook move, white will take at e6 and then push h7. For example:
1. …..Rg8 (Rb8/c3 etc. no better)
2. Re6
Obviously, h7 will lose since black takes at g7 with check and wins at h7 on the next move. Continuing:
2. …..Ke6
3. Kf4
Again, 3.h7 is going to lose to Rg7+. 3.Kh4 probably wins for white, too, but I can think of no reason not to put pressure on black’s e-pawn. Continuing:
3. …..Kf7 (Kf6 4.h7+-)
4. h7
Now, white must play this move- to do otherwise allows Kg6 winning both the h- and g-pawns and the game for black. Now, the game reduces to a king + pawn vs king endgame that is won for white:
4. …..Rg7
I am not going to show it, but any Nalimov tablebase will confirm that the line [Kg7 5.hg8(Q) Kg8 6.Ke4] is a won king/pawn ending for white. So, it is technically best for black to retain his rook vs the queen and pawn, but, of course, since white still has another pawn, it will be a fairly easy win for white regardless:
5. h8(Q) and white wins with ease with the extra pawn.
Back at move 1, black really has no choice but to sacrifice the knight for the g7 pawn:
1. g7 Ng7
2. hg7
Now, black has a choice, put the rook at g8 and try to exchange down, or simply guard g8 from another square along the 8th rank. The attempt to win g7 is going to lose for black, however, since white will win e4 and reduce down to a won king/pawn ending. For example:
2. …..Rg8 (with the idea of Kf6)
3. Ra5
This move is going to be required, I think. The problem is that if white protects with 3.Ra7, black need not give ground to white’s king with Kf6, but, rather, can play Kg5: [3.Ra7 Kg5 4.Rd7 Kf5 (or Re8 see lines below) 5.Kh4 Kf6 and, I can’t be absolutely sure this is won for white without playing a checking move from the fifth rank at some point]. There is a point to 3.Ra5 that took me a while to see:
3. …..Kf6 (Ke6 4.Rg5; Kg6 4.Kf4)
4. Kf4
This is the move that I had a hard time finding. Back at move 3 for black, he could have played Kg6, but it was easy to see that 4.Kf4 wins for white in that line since, if black takes with either the king or rook at g7, a rook check from g5 exchanges out the rooks and white wins the pawn at e4 and the game along with it. It wasn’t easy to see that the rooks can exchanged anyway after 3. ….Kf6 4.Kf4, or white can simply win at e4 while getting his rook to the g-file to support g7. Continuing:
4. …..Re8
Here, black will lose with either Kg7 (white plays Rg5+, exchanges rooks, and wins e4 pawn), or, if black takes with the rook at g7, then white plays Ra6+ followed by Ra7+ and exchanges at g7 (this is what I missed for about 20 minutes of frustration). Continuing:
4. …..Re8
5. Rg5
Supporting g7, and forcing the black rook back into his hole:
5. …..Rg8 (nothing holds now)
6. Rg4 and black’s last pawn will fall giving white, eventually, either connected passers in a rook endgame, or a pawn advantage in a king endgame. Either is won for white with proper play.
Back at move 2 for black, he needs to try some other rook move than Rg8. From the top:
1. g7 Ng7
2. hg7 Rd8
I don’t think it will matter if black plays Rd8 or some other move on the 8th rank like Rc8 or b8. Continuing:
3. Kh4
Hard to see anything better for white here. The king is going to head for h7. With this rook tied to the 8th rank, black is pretty limited in what he can do:
3. …..Rg8
I will look at the alternatives below after I finish with this line since one of them is quite involved and required a quite a lot of thought. Continuing:
4. Kh6 Kf4 (Rb8 5.Kh7 will win)
5. Rf6 Ke5
6. Rf8 wins for white.
I will continue this analysis in my next comment.
In my previous comment, I had analyzed the following line:
1. g7 Ng7
2. hg7 Rd8
3. Kh4
And I had shown that black loses with 3. ….Rg8. Black had two basic alternatives to Rg8 at move 3- either Rb8/c8, or Rd1. In the latter case, the idea is to mate white if he foolishly plays Kh5, but the move has other ideas, too, for hindering the advance of the g-pawn:
3. …..Rd1
4. Ra5
To force the king out of opposition square of f5 so that white might traverse h5.
4. …..Kf6
Here, [Kf4 5.Kh5!(5.g8Q Rh1 6.Kg6 Rg1 wins the new queen)Rg1 6.Kh6 Rg2 (Kf3 7.Rf5 wins) 7.Rh5 Rg1 8.Kh7 Kf3 9.Rf5 Ke2 10.g8Q Rg8 11.Kg8 wins since white holds onto his pawn]; and, of course, Ke6 loses to g8Q with check, and Kg6 loses to the same move. Now white needs to find a move here at move 5. He can’t play g8Q since black will check from h1 and g1 to win the new queen and probably lead to a draw. Also, playing Rg5 will lose the game to Rh1 followed by Rg1 with check. An under promotion with check seems to be called for here, and mostly because I have no other idea how to proceed:
5. g8(N) Kf7 (Kg7 6.Rg5 Kf7 7.Nh6)
6. Nh6 Kg6
7. Ra6 Kg7
8. Kg5 Rf1 (Rg1 9.Ng4)
9. Ra7 Kf8 (what else?)
10.Ng4 and white, having consolidated his position, should easily win the e-pawn while retaining his f-pawn and win the game. Finally, at move 3, black should still lose with a move like Rb8/c8:
3. …..Rb8
4. Kh5
Safe, now, since there is no mate threat against the white king:
4. …..Rb1
Else, the white king continues with Kh6 and Kh7. Continuing:
5. Ra5
Of course, not Kh6??. Continuing:
5. …..Kf6
Here, Kf4 is met by g8Q this time (white’s king is one square closer to g8 in this line)-[Kf4 6.g8(Q) Rh1 7.Kg6 Rg1 8.Kg6 Rg1 9.Kf7 Rg8 10.Kg8 Kf3 11.Rf5 holds the pawn]. Continuing:
6. g8(N) and this line is just like the previous line with an under promotion.
So, I think white clearly wins with 1.g7, but it ain’t easy over the board in a game. Did the white player in this game actually find the right continuations? I know I would have been completely at sea without the ability to move the pieces around, and unlimited time. I might have been able to play 1.g7, over the alternatives, but I am sure I couldn’t have found the other required continuations for white.
1.Rxe6 Kxe6 2.g7 Rg8 3.Kf4 Kf7 4.h7 Kxg7 5.hxg8=Q+ Kxg8 6.Kxe4, winning
Ha, my mind seems to work tonight! 🙂
Anyways, Rxe6 – Kxe6, g7 – Rg8, Kf4! – Kf6, h7 – Kxg7, hxg – Kxg8, Kxe4 and the resulting endgame is an easy win for white.
rxe5
1. g7! Rg8 (1…Ng7 2 hg7 Rg8 3 Ra7 is an easy win for White) 2 Re6! Ke6 3 Kf4 Kf7 4 h7 Kg7 5 hg8 Kg8 6 Ke4 +-
1. Re6?? does not work in view of … Ke6 2 g7 Rf3! 3 Kg4 Kf7 -+
-Justin Daniel
White take Knight, p g go ahead, Black B&Kinng try stop p, White King go to take p and after changing ppB. White win that clasicaly known ending.
amberas (takes 1 minute, was funny!)
My valentine told me to stop working on this puzzle so she can check mate me.
1.Rxe6! Kxe6 (if something else, g7 immediately wins) 2.g7 Rg8 3.Kf4 Kf7 4.h7 Kxg7 5.hxg8Q+ Kxg8 6.Kxe4 and white is winning here
2…Rg8 makes no sense. Analyse 2…Rf3+.
I think 2.h7 is the way to go, not 2.g7.