I like rook in g-file with the idea Rg8. Both sides will get queen, black first but white gets a lot af checks. Not solved, but an idea for a solution…
Well, I guess the first question one has to answer is- does white need to stop the pawns from from queening? If the answer is yes, then I think I see two possible approaches-1.Rg2/g3 or 1.Rf1 (giving up a rook for both pawns). Let’s look at the last of those first since it is the least obvious to me, and the least likely to work anyway:
Now, let’s look at the moves of a rook to the g-file at move 1 which threatens Rg8+. This looks promising to me since the bishop X-rays g8 through the pawn, so white can queen at g8 with check, even if black queens one of the pawns:
1. Rg2 e1(Q) (alternatives later) 2. Rg8 Ng8 3. fg8Q Ke7 4. Qf8 Kd7 5. Rf7 Kc6 6. Qc8 with mate on the next move.
So, at move 1, black must defend without queening a pawn since 1. …c1Q also is going to lead to mate in the same manner as above. He can underpromote the c-pawn with check:
1. Rg2 c1(N)+ 2. Kb2 Rb6
The alternatives I will cover later as I deal with the first move variations since white is locked into a particular line here, and those won’t be much different. Continuing:
3. Kc2
Of course, 3.Kc1?? loses to e1Q with check! I think black can answer Ka1/a3 with Ra6 safely: [3.Ka1 Ra6 4.Ba6?? e1Q! and the deflection of the bishop from the a2/g8 diagonal is now fatal to white.] Continuing:
3. …..e1(N)
I see nothing else here that I won’t actually deal with later in the first move variations. With the second underpromotion, black has now successfully forked a rook. Continuing:
4. Kc1 Ng2 (Nf3 loses of course) 5. Rg3 Ng6 6. Rg2 Rf6 7. Kd2 Rf6 8. Rg6 Rd7 is a known draw. Also, at move 8, white only gets a draw with 8.Bf7 Kf7 since the R vs N ending is drawn. So, I don’t think I need to look at the first move variations here.
However, this wasn’t a waste- the knight fork at move 3 was a key defense for black here. White might prevent this by playing 1.Rg3 at the first move. Let’s play it out and see where this gets us:
1. Rg3 c1(N)+ 2. Kb2 Rb6 3. Kc2 e1(N)+ 4. Kc1 Ng6 (what else better?) 5. Re2 and the double threat of Rxe1 and Re8+ are fatal to black. So, he cannot underpromote at move 1. Let’s now consider some alternative moves at move 1 for black.
1. Rg3 Ra6
Here, black cannot defend with Ng6: [1. …Ng6?? 2.Rg1! and white will win both black pawns safely and win the game]. Also, 1. …Rg6 should lose to 2.Rh3 quite cleanly: [1. …Rg6 2.Rh3! c1N 3.Kb1 Rb6 4.Kc2 e1N 5.Kc1 Ng6 6.Re2 should win easily, too, as before]. Continuing from 1. …Ra6 above:
2. Kb3
Here, Bxa6 simply takes the bishop off the key diagonal into g8: [2.Ba6? e1Q! 3.Rg8 Ng8 4.fg8 Kg8 5.Bc4! Kg7 6.Rc2 draws only for either side, I believe. Continuing:
2. …..Ra3
I don’t see another defense here. The idea, of course, is to force the white king onto a square where black can queen a pawn with check. Continuing:
3. Kc2
White might well lose with 3.Ka3: [3.Ka3? c1Q 4.Kb3 Qd1 5.Kb2 Qd4 6.Kc2 and I don’t want to go too deep here needlessly, but white will struggle to find a non-losing line here]. Continuing:
3. …..Rg3 4. Re2 Rf3
Or 4.Be2 Rg7 5.Bc4 Nc6 6.Kc3 Ne5 with a clean draw.
So, right now, I don’t see how either rook move the g-file on move 1 can win this for white. I need to think about this some more.
Ok, there is a third way to threaten the back rank- 1.Ra3:
1. Ra3 Rc6 (alternatives below) 2. Rh3
And now black has a real problem- how to prevent Rh8+. He can try Ng6, he can try the underpromotion at c1, or he can check from a6. I don’t see any of these working but maybe this line, though I don’t think so:
2. …..Ng6 3. Re3 c1(Q)
The alternatives are no good, I think- [3. …Ne7 4.Rxe7 Ke7 5.f8Q+]. I will cover 3. …Kg7 later since it seems rather complex to me right now, as well as c1(N). Continuing:
4. Re8 Kg7 5. Rg8! Kh7
Here, 5. …Kh6 allows white to queen his pawn: [5. …Kh6? 6.f8Q Kg5 (or 6. …Nf8 7.Rh2#; or 6. …Kh5 7.Be2+-) 7.Qf5 Kh4 (or 7. …Kh6 8.Qh3 Rh2+-) 8.Rh2 Kg3 9.Qf2 Kg4 10.Be2+-]. Continuing:
6. Rh2 Qh6 (or get mated)
And now the critical decision in this line for white. I can’t make Rh6 work- black still threatens e1Q, and f8 is under the guard of the knight- this lead to look at 7.Rg6 so that f8 can be played, and I now think this is right:
7. Rg6! Ra6
Nothing seems better: [7. …Qh2 8.f8N! Kh8 9.Rg8#]; or [7. …Rg6 8.Rh6! Kg7! (or 8. …Rh6 9.f8Q! Ra6 10.Ba6! e1Q 11.Bd3+-) 9.Rh1 with a winning endgame]; or [7. …Kg6 8.Rh6 Kg7 9.Rh8! Rf6 10.Re8 Rf2 11.Ka3 with another winning endgame]. Continuing:
8. Ba6
What follows in this line was probably the main idea the composer had in mind when he set out to compose it. This is an utterly amazing position. I am now pretty sure white must capture at a6 to win, but win he will, though this wasn’t easy to find, even with the chess board out. Continuing:
8. …..Qh2 (Kg6 9.Rh6 Kh6 10.f8Q+)
And now for the capstone move. In this position, black is threatening to queen the e-pawn with check (discovered), but white has an absolutely amazing reply here that wins in all variations:
9. Bd3!!
And what can black do? Kh8 allows f8Q followed by mate, any move of the queen is going to allow a discovered check either taking the queen on the move, or allowing Rf6 followed by f8Q with check and/or mate. So, black has e1Q or e1N:
9. …..e1Q 10.Rg2!
The point for me of 9.Bd3 is to play this block with check. Black is toast- either king move allows f8Q with check followed by a mate by the queen either on the g-file or the h-file. The underpromotion at move 9 is the only possible defense, but this also fails to hold:
9. …..e1N 10.Rg2! Nd3 (or get mated) 11.f8(N)!
The last critical move in this line is to make sure the endgame is winnable. A hasty 11.Rh2+ allows black to liquidate the f-pawn since the knight has f2 covered and white can only protect from h7: [11.Rh2? Kg7 12.Rh7 Kf8! 13.Kb3 Ne5! followed by 14. …Nxf7.] Continuing from 11.f8(N) above:
11. ….Kh6/h8 12. Rh2 Kg7 13. Nd7 with a winning endgame of R+N vs N.
I really wish I could end it right here. I am deeply afraid I will find a hole in the moves above at moves 1 or 3, which will be a huge disappointment after finding this main line above.
I now need to fill in the holes at moves 1-3. I will work backwards starting with move 3:
1. Ra3 Rc6 2. Rh3 Ng6 3. Re3
Here, black has different moves open to him. I think I dealt with Ne7 in the previous comment, but not the following alternatives: c1(N)+, Rc8, Kg7, Rc4, and Ra6+. Continuing:
Variations with 3. …c1(N):
1. Ra3 Rc6 2. Rh3 Ng6 3. Re3 c1(N) 4. Kb2 Rb6
Here, I feel pretty certain that moves like 4. …Rc4 or Rc8 are going to be essentially the same as the line below that analyze the same move as the 3rd move alternatives. Continuing:
5. Kc1 Kg7 6. Rfe2 and this is surely won for white.
Variations with 3. …Rc8:
1. Ra3 Rc6 2. Rh3 Ng6 3. Re3 Rc8 4. Re8! Re8 (what else better?) 5. fe8Q Ke8 6. Re2! and with check meaning the last black pawn falls leaving him in a losing R+B vs N ending.
In my previous comment, I outline a similar variation for 5. …Kh6 where white can queen the pawn and use the mate threat to prevent black from capturing at f8- this holds here as well: [5. …Kh6 6.f8Q! Kh5 7.Qf5 Kh4 8.Rh2 Kg3 9.Qf2 Kg4 10.Rg6#]. Continuing:
6. Rh2 Nh4 (Rh4 7.Rh4 Nh4 8.f8Q+-) 7. f8Q c1N (what else better?) 8. Kb1 and there can’t possibly be a defense to the mate here.
The line I am most worried about, but I think white can just queen his pawn now:
4. f8(Q)Nf8 (or mate on next move) 5. Rf7
I think this probably the only way forward. Earlier, when I looked at this line, I was thinking 5.Rg3, but had overlooked black’s rook covering g6 allowing black to block the check successfully with Ng6. However, Rf7 wasn’t hard to find with the right motivation, though it is difficult prove out:
5. …..Kh6
Nothing really better here: [5. …Kg8/h8 6.Re8! and black has nothing but delays to the coming mate of Rexf8]; or [5. …Kg6 6.Rg3! Kh5 7.Be2 Kh4 8.Rg4 Kh3 (or 8. …Kh5 9.Rc4+!) 9.Rf3!!+-]. Continuing:
6. Rh3 Kg5 7. Rg3 Kh4 8. Rg1
I don’t see another move here for white- he must now cover the 1st rank, but he now has a winning position. Continuing:
The last trick in this line. At first I thought R8g4 wins like in the variation in the note above, but then I saw Nd3 is going to win a rook at e1 or white just gives a perpetual. However, Rf8 removes this last thorn effectively:
Earlier today, I did a partial analysis of the following line:
1. Ra3 Rc6 2. Rh3
And I think I showed conclusively that white wins when black replies at move 2 with Ng6 to prevent Rh8. Ng6 was only the most obvious reply I could see, but not the only possible one. Black could check from a6, underpromote with check on c1(N), or play a move like Rc8, but I think these also all lose:
2. …..c1(N) 3. Kb1
And now what? Moves like Ng6, Rb6, Rc4, Rb6 are just transpositions of lines I analyzed earlier. Let’s move on 2. …Rc8:
2. …..Rc8 3. Rh8 Kg7 (Ng8 mates quicker) 4. Rc8!
If white tries f8Q, black will get time to queen a pawn. Now, black still can do so, but white will then queen with check. Continuing:
4. …..Ng6 (otherwise f8Q+ wins) 5. Rg8
A theme seen earlier more than once:
5. …..Kh6 (Kh7 6.Rh2+-) 6. f8(Q) and we saw similar lines earlier that were all mates with even less black material on board. It is pretty clear there are no defenses at move 2 for black.
Finally, let’s make sure black had no replies at move 1 that were better:
1. Ra3 Ng6 2. Ra8 Ke7 (Kg7 below) 3. Re2 and white can win simply with 4.Rxc2 as well. In this line, however, the king can go to g7 at move 2:
2. …..Kg7 3. Rg8 Kh7 4. Rg6
This line is similar to one I discussed earlier. White is now threatening f8(N) followed by Rg8#. Continuing:
4. …..Rg6 (nothing better) 5. f8(Q) and mate will soon follow since a black queen at c1 or e1 won’t matter in this position.
Or, at move 1, black has a more testing reply:
1. Ra3 c1(N) 2. Ka1!
This might be the only winning path, though I haven’t been really thorough in this case. At first I did what I did earlier and played Kb1, but then I realized that black could pin the bishop and capture with check in some lines [2.Kb1? Rb6 3.Kc2 Rc6! 4.Ra8 Nc8! and now how can white win this? I tried what looks like everything reasonable and came up with nothing]. However, 2.Ka1 wins convincingly:
2. …..Rc6 (Nb3 3.Kb2! wins) 3. Rh3! Nb3
I have already analyzed variations with moves like Ra6 and Ng6, and found them all losing for black. Continuing:
4. Kb2!
Of course, Bb3 or Rb3 allows black to queen the e-pawn with check. Continuing:
4. …..Ng6 (what else now?) 5. Re3 and I have already covered this ground extensively in almost identical positions.
Or, at move 1:
1. Ra3 Nc8 2. Rg3! and I covered a similar line in my very first comment, but white is now a move ahead than he was before, and the extra move is now fatal to black- there is no defense to the coming Rg8+.
I don’t think black has a viable defense to 1.Ra3.
I believe this is the essential commencing sequence. The white pawn is lost in an exchange and white is left with a rook and bishop endgame. If I am careful, I can make this work without a stalemate!
To Yancey Ward: I didn’t dive by far so deep into this puzzle as you. Only want to mention that I also looked at 1. Ra3, but thought Ng6 would be blacks best defence and didn’t find a convincing continuation after that. A variation I looked at was:
Well, I looked a bit too quick at it yesterday. Reviewing it now, g7 wasn’t a good hidingplace for black king after all, because of Rg8+ and RxNg6. And Ke7 doesn’t look too good either, white has a lot of checks before black even has a queen.
So I probably have to assume that Ng6 wasn’t a very good answer to Ra3, which may well be the right solution then.
I like rook in g-file with the idea Rg8.
Both sides will get queen, black first but white gets a lot af checks.
Not solved, but an idea for a solution…
Amongst several lines, there could be:
1. Rg2 Rh8
2. Ra3
Not Rg3, and not Rb3? c1=N.
2. … Nd5
3. Bxd5 Ke7
4. Rg8 c1=Q
5. f8=Q etc.
Well, I guess the first question one has to answer is- does white need to stop the pawns from from queening? If the answer is yes, then I think I see two possible approaches-1.Rg2/g3 or 1.Rf1 (giving up a rook for both pawns). Let’s look at the last of those first since it is the least obvious to me, and the least likely to work anyway:
1. Rf1
Covers e1 and c1:
1. …..ef1(Q)
2. Rf1 Rc6
3. Kb3 Nd5
4. Rg1
What else here? Continuing:
4. …..c1(Q)
5. Rc1 Ne3
6. Rc3 Nc4
7. Rc4 Rc4 draws.
Now, let’s look at the moves of a rook to the g-file at move 1 which threatens Rg8+. This looks promising to me since the bishop X-rays g8 through the pawn, so white can queen at g8 with check, even if black queens one of the pawns:
1. Rg2 e1(Q) (alternatives later)
2. Rg8 Ng8
3. fg8Q Ke7
4. Qf8 Kd7
5. Rf7 Kc6
6. Qc8 with mate on the next move.
So, at move 1, black must defend without queening a pawn since 1. …c1Q also is going to lead to mate in the same manner as above. He can underpromote the c-pawn with check:
1. Rg2 c1(N)+
2. Kb2 Rb6
The alternatives I will cover later as I deal with the first move variations since white is locked into a particular line here, and those won’t be much different. Continuing:
3. Kc2
Of course, 3.Kc1?? loses to e1Q with check! I think black can answer Ka1/a3 with Ra6 safely: [3.Ka1 Ra6 4.Ba6?? e1Q! and the deflection of the bishop from the a2/g8 diagonal is now fatal to white.] Continuing:
3. …..e1(N)
I see nothing else here that I won’t actually deal with later in the first move variations. With the second underpromotion, black has now successfully forked a rook. Continuing:
4. Kc1 Ng2 (Nf3 loses of course)
5. Rg3 Ng6
6. Rg2 Rf6
7. Kd2 Rf6
8. Rg6 Rd7 is a known draw. Also, at move 8, white only gets a draw with 8.Bf7 Kf7 since the R vs N ending is drawn. So, I don’t think I need to look at the first move variations here.
However, this wasn’t a waste- the knight fork at move 3 was a key defense for black here. White might prevent this by playing 1.Rg3 at the first move. Let’s play it out and see where this gets us:
1. Rg3 c1(N)+
2. Kb2 Rb6
3. Kc2 e1(N)+
4. Kc1 Ng6 (what else better?)
5. Re2 and the double threat of Rxe1 and Re8+ are fatal to black. So, he cannot underpromote at move 1. Let’s now consider some alternative moves at move 1 for black.
1. Rg3 Ra6
Here, black cannot defend with Ng6: [1. …Ng6?? 2.Rg1! and white will win both black pawns safely and win the game]. Also, 1. …Rg6 should lose to 2.Rh3 quite cleanly: [1. …Rg6 2.Rh3! c1N 3.Kb1 Rb6 4.Kc2 e1N 5.Kc1 Ng6 6.Re2 should win easily, too, as before]. Continuing from 1. …Ra6 above:
2. Kb3
Here, Bxa6 simply takes the bishop off the key diagonal into g8: [2.Ba6? e1Q! 3.Rg8 Ng8 4.fg8 Kg8 5.Bc4! Kg7 6.Rc2 draws only for either side, I believe. Continuing:
2. …..Ra3
I don’t see another defense here. The idea, of course, is to force the white king onto a square where black can queen a pawn with check. Continuing:
3. Kc2
White might well lose with 3.Ka3: [3.Ka3? c1Q 4.Kb3 Qd1 5.Kb2 Qd4 6.Kc2 and I don’t want to go too deep here needlessly, but white will struggle to find a non-losing line here]. Continuing:
3. …..Rg3
4. Re2 Rf3
Or 4.Be2 Rg7 5.Bc4 Nc6 6.Kc3 Ne5 with a clean draw.
So, right now, I don’t see how either rook move the g-file on move 1 can win this for white. I need to think about this some more.
Ok, there is a third way to threaten the back rank- 1.Ra3:
1. Ra3 Rc6 (alternatives below)
2. Rh3
And now black has a real problem- how to prevent Rh8+. He can try Ng6, he can try the underpromotion at c1, or he can check from a6. I don’t see any of these working but maybe this line, though I don’t think so:
2. …..Ng6
3. Re3 c1(Q)
The alternatives are no good, I think- [3. …Ne7 4.Rxe7 Ke7 5.f8Q+]. I will cover 3. …Kg7 later since it seems rather complex to me right now, as well as c1(N). Continuing:
4. Re8 Kg7
5. Rg8! Kh7
Here, 5. …Kh6 allows white to queen his pawn: [5. …Kh6? 6.f8Q Kg5 (or 6. …Nf8 7.Rh2#; or 6. …Kh5 7.Be2+-) 7.Qf5 Kh4 (or 7. …Kh6 8.Qh3 Rh2+-) 8.Rh2 Kg3 9.Qf2 Kg4 10.Be2+-]. Continuing:
6. Rh2 Qh6 (or get mated)
And now the critical decision in this line for white. I can’t make Rh6 work- black still threatens e1Q, and f8 is under the guard of the knight- this lead to look at 7.Rg6 so that f8 can be played, and I now think this is right:
7. Rg6! Ra6
Nothing seems better: [7. …Qh2 8.f8N! Kh8 9.Rg8#]; or [7. …Rg6 8.Rh6! Kg7! (or 8. …Rh6 9.f8Q! Ra6 10.Ba6! e1Q 11.Bd3+-) 9.Rh1 with a winning endgame]; or [7. …Kg6 8.Rh6 Kg7 9.Rh8! Rf6 10.Re8 Rf2 11.Ka3 with another winning endgame]. Continuing:
8. Ba6
What follows in this line was probably the main idea the composer had in mind when he set out to compose it. This is an utterly amazing position. I am now pretty sure white must capture at a6 to win, but win he will, though this wasn’t easy to find, even with the chess board out. Continuing:
8. …..Qh2 (Kg6 9.Rh6 Kh6 10.f8Q+)
And now for the capstone move. In this position, black is threatening to queen the e-pawn with check (discovered), but white has an absolutely amazing reply here that wins in all variations:
9. Bd3!!
And what can black do? Kh8 allows f8Q followed by mate, any move of the queen is going to allow a discovered check either taking the queen on the move, or allowing Rf6 followed by f8Q with check and/or mate. So, black has e1Q or e1N:
9. …..e1Q
10.Rg2!
The point for me of 9.Bd3 is to play this block with check. Black is toast- either king move allows f8Q with check followed by a mate by the queen either on the g-file or the h-file. The underpromotion at move 9 is the only possible defense, but this also fails to hold:
9. …..e1N
10.Rg2! Nd3 (or get mated)
11.f8(N)!
The last critical move in this line is to make sure the endgame is winnable. A hasty 11.Rh2+ allows black to liquidate the f-pawn since the knight has f2 covered and white can only protect from h7: [11.Rh2? Kg7 12.Rh7 Kf8! 13.Kb3 Ne5! followed by 14. …Nxf7.] Continuing from 11.f8(N) above:
11. ….Kh6/h8
12. Rh2 Kg7
13. Nd7 with a winning endgame of R+N vs N.
I really wish I could end it right here. I am deeply afraid I will find a hole in the moves above at moves 1 or 3, which will be a huge disappointment after finding this main line above.
In my previous comment, I outlined a very pretty variation:
1. Ra3 Rc6
2. Rh3 Ng6
3. Re3 c1(Q)
4. Re8 Kg7
5. Rg8 Kh7
6. Rh2 Qh6
7. Rg6 Ra6
8. Ba6 Qh2
9. Bd3 e1(N)
10.Rg2 Nd3
11.f8N Kh6
12.Rh2+-
I now need to fill in the holes at moves 1-3. I will work backwards starting with move 3:
1. Ra3 Rc6
2. Rh3 Ng6
3. Re3
Here, black has different moves open to him. I think I dealt with Ne7 in the previous comment, but not the following alternatives: c1(N)+, Rc8, Kg7, Rc4, and Ra6+. Continuing:
Variations with 3. …c1(N):
1. Ra3 Rc6
2. Rh3 Ng6
3. Re3 c1(N)
4. Kb2 Rb6
Here, I feel pretty certain that moves like 4. …Rc4 or Rc8 are going to be essentially the same as the line below that analyze the same move as the 3rd move alternatives. Continuing:
5. Kc1 Kg7
6. Rfe2 and this is surely won for white.
Variations with 3. …Rc8:
1. Ra3 Rc6
2. Rh3 Ng6
3. Re3 Rc8
4. Re8! Re8 (what else better?)
5. fe8Q Ke8
6. Re2! and with check meaning the last black pawn falls leaving him in a losing R+B vs N ending.
Variations with 3. …Rc4:
1. Ra3 Rc6
2. Rh3 Ng6
3. Re3 Rc4
4. Re8 Kg7
5. Rg8 Kh7
In my previous comment, I outline a similar variation for 5. …Kh6 where white can queen the pawn and use the mate threat to prevent black from capturing at f8- this holds here as well: [5. …Kh6 6.f8Q! Kh5 7.Qf5 Kh4 8.Rh2 Kg3 9.Qf2 Kg4 10.Rg6#]. Continuing:
6. Rh2 Nh4 (Rh4 7.Rh4 Nh4 8.f8Q+-)
7. f8Q c1N (what else better?)
8. Kb1 and there can’t possibly be a defense to the mate here.
Variations with 3. …Ra6:
1. Ra3 Rc6
2. Rh3 Ng6
3. Re3 Ra6
4. Ba6 c1(Q) (what else now?)
5. Re8 Kg7
6. Rg8 Kh7 (see above for Kh6)
7. Rh2 Qh6 (or mate in 2 more)
8. Rh6 Kh6
9. Be2 wins easily.
Variations with 3. …Kg7:
1. Ra3 Rc6
2. Rh3 Ng6
3. Re3 Kg7
The line I am most worried about, but I think white can just queen his pawn now:
4. f8(Q)Nf8 (or mate on next move)
5. Rf7
I think this probably the only way forward. Earlier, when I looked at this line, I was thinking 5.Rg3, but had overlooked black’s rook covering g6 allowing black to block the check successfully with Ng6. However, Rf7 wasn’t hard to find with the right motivation, though it is difficult prove out:
5. …..Kh6
Nothing really better here: [5. …Kg8/h8 6.Re8! and black has nothing but delays to the coming mate of Rexf8]; or [5. …Kg6 6.Rg3! Kh5 7.Be2 Kh4 8.Rg4 Kh3 (or 8. …Kh5 9.Rc4+!) 9.Rf3!!+-]. Continuing:
6. Rh3 Kg5
7. Rg3 Kh4
8. Rg1
I don’t see another move here for white- he must now cover the 1st rank, but he now has a winning position. Continuing:
8. …..Rc4 (what else better?)
9. Rf8! c1(N)
Or [9. …Rg4 10.Rh8 Kg5 11.Rg8 Kf5 12.R8g4!+-]; or [9. …Kh3 10.Rh8 Rh4 11.Rh4 Kh4 12.Kb2 Kh3 13.Kc2 Kh2 14.Re1+-]. Continuing:
10.Kb1 Rg4 (Kh3 11.Rh8 Rh4 12.Rh4)
11.Rh8 Kg5
12.Rg8 Kf5
13.Rf8!
The last trick in this line. At first I thought R8g4 wins like in the variation in the note above, but then I saw Nd3 is going to win a rook at e1 or white just gives a perpetual. However, Rf8 removes this last thorn effectively:
13. ….Ke5 (Kg5 14.Rc1 Re4 15.Re1)
14.Re8 Kf5
15.Rc1 wins easily.
I will have to deal with the 2nd and 1st move alternatives later. I am exhausted right now, and have spent the last 3 hours on this.
Earlier today, I did a partial analysis of the following line:
1. Ra3 Rc6
2. Rh3
And I think I showed conclusively that white wins when black replies at move 2 with Ng6 to prevent Rh8. Ng6 was only the most obvious reply I could see, but not the only possible one. Black could check from a6, underpromote with check on c1(N), or play a move like Rc8, but I think these also all lose:
2. …..c1(N)
3. Kb1
And now what? Moves like Ng6, Rb6, Rc4, Rb6 are just transpositions of lines I analyzed earlier. Let’s move on 2. …Rc8:
2. …..Rc8
3. Rh8 Kg7 (Ng8 mates quicker)
4. Rc8!
If white tries f8Q, black will get time to queen a pawn. Now, black still can do so, but white will then queen with check. Continuing:
4. …..Ng6 (otherwise f8Q+ wins)
5. Rg8
A theme seen earlier more than once:
5. …..Kh6 (Kh7 6.Rh2+-)
6. f8(Q) and we saw similar lines earlier that were all mates with even less black material on board. It is pretty clear there are no defenses at move 2 for black.
Finally, let’s make sure black had no replies at move 1 that were better:
1. Ra3 Ng6
2. Ra8 Ke7 (Kg7 below)
3. Re2 and white can win simply with 4.Rxc2 as well. In this line, however, the king can go to g7 at move 2:
2. …..Kg7
3. Rg8 Kh7
4. Rg6
This line is similar to one I discussed earlier. White is now threatening f8(N) followed by Rg8#. Continuing:
4. …..Rg6 (nothing better)
5. f8(Q) and mate will soon follow since a black queen at c1 or e1 won’t matter in this position.
Or, at move 1, black has a more testing reply:
1. Ra3 c1(N)
2. Ka1!
This might be the only winning path, though I haven’t been really thorough in this case. At first I did what I did earlier and played Kb1, but then I realized that black could pin the bishop and capture with check in some lines [2.Kb1? Rb6 3.Kc2 Rc6! 4.Ra8 Nc8! and now how can white win this? I tried what looks like everything reasonable and came up with nothing]. However, 2.Ka1 wins convincingly:
2. …..Rc6 (Nb3 3.Kb2! wins)
3. Rh3! Nb3
I have already analyzed variations with moves like Ra6 and Ng6, and found them all losing for black. Continuing:
4. Kb2!
Of course, Bb3 or Rb3 allows black to queen the e-pawn with check. Continuing:
4. …..Ng6 (what else now?)
5. Re3 and I have already covered this ground extensively in almost identical positions.
Or, at move 1:
1. Ra3 Nc8
2. Rg3! and I covered a similar line in my very first comment, but white is now a move ahead than he was before, and the extra move is now fatal to black- there is no defense to the coming Rg8+.
I don’t think black has a viable defense to 1.Ra3.
1. R-f1 PxR/Q
2. RxQ …
I believe this is the essential commencing sequence. The white pawn is lost in an exchange and white is left with a rook and bishop endgame. If I am careful, I can make this work without a stalemate!
To Yancey Ward:
I didn’t dive by far so deep into this puzzle as you.
Only want to mention that I also looked at 1. Ra3, but thought Ng6 would be blacks best defence and didn’t find a convincing continuation after that.
A variation I looked at was:
1. Ra3 Ng6
2. Ra8+ Kg7
3. Rg2 (what else?) c1=Q
4. Rxg6+ Kxg6!
5. f8=Q (or Ra6+ Kg7 Rxh6 Kxh6 f8=Q) Qxc4+
Is here an improvement I have overlooked for white in that line?
Well, I looked a bit too quick at it yesterday. Reviewing it now, g7 wasn’t a good hidingplace for black king after all, because of Rg8+ and RxNg6.
And Ke7 doesn’t look too good either, white has a lot of checks before black even has a queen.
So I probably have to assume that Ng6 wasn’t a very good answer to Ra3, which may well be the right solution then.