White to move and win.
This was recently posted by Magnus Carlsen.
Chess Daily News from Susan Polgar
Absolutely brilliant endgame
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White to move and win.
This was recently posted by Magnus Carlsen.
I want to know the solution.
I see two somewhat obvious beginnings here, but I guess we should start with the most obvious one:
1. Re3 Kb4
Clearly, 1. …a2 is going to lose to 2.Ra3 since, after 2. …Kb4, 3.Ra2 is going to shut the black king out because of the pawn on c2. So, black must move the king to get control of a3. This, of course, suggests the other obvious beginning for white, though I will leave that for the following comment. Continuing
2. Kd2
The idea is to attempt to bring the king to b1, or threaten to, to contain the black a-pawn/s. However, black can foil this plan:
2. …..a2! (the only draw)
3. Re1
Now, or later. I am not even sure that white holds with any other move, though I haven’t looked too long at moves like 3.c3 and 3.Re4+, but Re1 seems to be required in those, too, just on the face of it. Continuing:
3. …..Ka3
4. Kc3
Anything else here better? Continuing:
4. …..d5
I think the position is such that black can draw with other pawn moves like a4 and d6- the white rook is anchored to the 1st rank and the white king is anchored to c3 to prevent Kb2- white in a sort of zugzwang. I just prefer d5 since it brings about the key position more quickly. Continuing:
5. Rd1 a4!
It is important to not play 5. …d4 here since white will capture at d4 and then play c4 when black plays Kb2 and white will queen a full move ahead of black to win the game since black will lose a tempo moving his king off of a1 after white gives up the rook there. With 5. …a4, black gains the extra tempo because white’s king and rook are tied down, and black can now draw the game:
6. Re1 d4!
7. Kd4 Kb2!
8. c4 a1Q
9. Ra1 Ka1
10.c5 a3
11.c6 a2
12.c7 Kb1
13.c8Q a1Q with a clean draw.
With the importance of 1.Kb4, it should occur to try a different beginning for white.
Full source:
Katsnelson V & Katsnelson L, Uralski Problemi, third special prize Dvoretsky 60 JT
It is rather good news that top-class players are interested in studies.
The setting of this one is very game-like.
To win, White uses a very old idea from Polerio (1590 !)
1Re3 kb4 2Rb3+ ka4 3Rb1 a2 4Ra1ka3
5Kd2 kb2 6kd1ka1 7Kc1 & c pawn queens
Te4,Kb5
c4+,Ka4
c5+,kb5
Txe3,kb4
kd3,kb3
kd2+kb2
Tc3,a4
Tc1,a2
Ta1,a3
kd3,kb3
ke3,kb2
kd2,kb3
kc1,kc4
kc2,kb4
Txa2,kc4
Txa3,kxc5
Ta6,kd4
ke4,Txd7
Te4,kb5
c4+,ka4
c5+,kb5
Txe3,kb4
kd3,kb3
kd2+,kb2
Tc3,a4
Tc1,a2
Ta1,a3
Kd3,kb3
ke3,kb2
kd2,kb3
kc1,kc4
Txa3,kxc5
Ta6,kd4
I forgot to mention the year of this study : 2007
This comment has been removed by the author.
In my previous comment, I examined 1.Re3 and I showed, I think, that black obtains a draw with 1. …Kb4. So, can white cut off the black king by playing 1.Re4 first? While this move occurred to me very early on (within the first minute of studying the problem), it has turned out to be much more involved than I initially thought. First, white can’t really prevent Kb4, but it is critical that he delay it in order to advance the c-pawn to c5.
1. Re4
This threatens Ra4 winning the a3 pawn and the game, and I think black has only one move:
1. …..Kb5
So, what can white do here? He can’t play 2.Re3 for the same reasons as before- black plays Kb4. He can’t play Kxe3 either, since black wins with a2, as will be the case with any king move. This leaves the two pawn moves, but 2.c3 is going to lose to a2 as well, so white must try 2.c4+:
2. c4 Kb4 (alternatives later)
3. c5
The same considerations apply at move 3 as for move 2 for white- the threat of a2 basically forces white to make a checking move. Continuing:
3. …..Kc5 (alternatives later)
4. Ra4 d5 (alternative later)
5. Ra3 Kb4 (what else?)
6. Re3 a4
Now, with the last white pawn off the board, white must preserve the rook to win, so black’s goal is to force white to give it up for a queening pawn. Continuing:
7. Kd2
The natural looking move to me- I want to keep the black king out of b3 as long as possible. Continuing:
7. …..d4
Most of the alternatives are going to transpose at some point now. I see the major alternative here to be the push of a3. I am not going to demonstrate all of the lines and variations, but even an average player should be able to work them out based on what I show here: [7. …a3 8.Kc2 a2 9.Kb2 Kc4 10.Ka2 d4 11.Rh3 d3 12.Kb2+-]. Continuing from 7. …d5 above:
8. Rh3 a3 (what else?)
9. Kc2
Only this or Kc1 win. Continuing:
9. …..a2 (Ka4 10.Rd3 wins)
10.Kb2 a1Q (Kc4 loses as above)
11.Ka1 Kc4
12.Kb2 d3 (what else?)
13.Kc1 Kc3
14.Kd1 and white will win the pawn eventually with a double attack on it.
So, let’s back up to move 4 in the line above for black’s major alternative. (For reference, this is the line-1.Re4 Kb5 2.c4 Kb4 3.c5 Kc5 4.Ra4). Continuing:
4. …..Kb5
5. Ra3 Kb4
Here, most of the alternatives are basically uninteresting based on what we have seen previously. If black doesn’t attack the rook, white takes at e3 and moves the king to d3: [5. …a4 6.Ke3 Kb4 7.Ra1! Kb3 8.Kd3 a3 9.Rb1! Ka4 (or 9. …Ka2 10.Kc2 d6 11.Rd1 d5 12.Rd5 Ka1 13.Kb3 any 14.Rd1#) 10.Kc3 a2 11.Rd1 Ka3 12.Kc2 d5 13.Rd5 a1N 14.Kc3 Ka4 15.Rd4 Kb5 16.Rd1+-]. Continuing from 5. …Kb4 above:
6. Ra1 a4
7. Ke3 Kb3
8. Kd3 a3
9. Rb1! and we have seen the rest in the parenthetical variation after 5. …Kb4 above.
Due to problems of comment length, I will continue in the next comment, starting with the variations at move 3 for black in the line above, and I warn- it is the difficult part of this problem.
In my previous comment, I analyzed the following line:
1. Re4 Kb5
2. c4 Kb4 (alternatives later)
3. c5 Kc5
And, I think I showed conclusively that white wins after 4.Ra4. However, black does not need to lose time and capture at c5 at move 3. Let’s work through those variations now:
3. …..Kb3
Obviously the most natural of black’s moves here, and the most troublesome for me. Black’s king is making for b2, and I have to admit it took me a long time yesterday and today to fully work this out. I had in my head the major themes already- especially the set up of the white c-pawn and black d-pawn (if white can force black to play d6/d5, white can then pass by with c6 to queen and win), along with various mating possibilities if white gets black’s king trapped on a2/a1. However, putting the pieces together was difficult. Continuing from 3. …Kb3 above:
4. Re3!
Not possible to play any other move here since black is threatening a2 if he doesn’t have to move the king. Only 4.Re3 forces the king to move. Continuing:
4. …..Kb2
The variations here are uninteresting to us now since we have seen highly similar lines in the previous comment. Simply put, black’s king cannot retreat to the 4th rank without allowing white’s king to take control at b2/c2/d2. Black must move forward. Continuing:
5. Kd3!
The only winning move, I think. There are several ideas in play here. With his c-pawn still on the board, white always has the possibility to sacrifice the rook at a1 when necessary while his king positions himself to win the backward a-pawn and the d-pawn in order to queen the c-pawn. Also, there are ideas of checking from e2 and bringing the king to c3/b3 for some mating threats in addition to the ideas of trapping the black king on a2/a1. Continuing from 5.Kd3 above:
5. …..a2 (alternatives later)
6. Re2! Kb3 (alternatives later)
7. Re1 Kb2
8. Ra1!
Not a hard move to find if you have dealt with this type of zugzwang position/problem before. The rook is immune since, if black takes at a1, white will play Kc2 and will then play Kc1-Kc2 repeatedly as black runs out of moves and is forced to play d6/d5 at which point white plays c6, and there is a stinger at the end that foils the check by the black d-pawn: [8. …Ka1 9.Kc2 a4 10.Kc1 a3 11.Kc2 d5 12.c6! d4 13.c7 d3 14.Kd3 Kb2 15.c8Q a1Q 16.Qc2#]. Continuing from 8.Ra1 above:
8. …..Kb3
Nothing is really going to work here. A sort of zugzwang is already in force here. Black will never be able to capture at a1 as long as white’s king maintains contact with c2 or c1 for the reasons outlined above, and white will just wait black out. Continuing:
9. Kd2 Kb2
10.Kd1
And, now, the black king cannot be moved without allowing the white king to take up residence at c1, and white will again wait out black’s moves:
10. ….a4
Or [10. …Kb3 11.Kc1 a4 12.Kd1 Kb2 13.Kd2 Kb3 (or 13. …a3 14.Kd1 Kb3 15.Kc1+-) 14.Kc1 a3 (or 14. …Ka3 15.Kc2+-) 15.Kd1 Kb2 16.Kd2 Kb3 17.Kc1+-]. Continuing:
11.Kd2
Again, just waiting for black to make the fatal moves. Continuing:
11. ….a3
12.Kd1 Kb3
13.Kc1!
And now the forward black a-pawn must be lost due to the zugzwang. And black cannot win the c-pawn without also immediately dropping the other a-pawn. The rest is trivial and left for the curious.
So now, we must back up to move 6 to work out black’s alternatives at that point. For reference, we are discussing the following line: (1.Re4 Kb5 2.c4 Kb4 3.c5 Kb3 4.Re3 Kb2 5.Kd3 a2 6.Re2):
6. …..Kb1 (Ka1 7.Kc2 a4 8.Re1#)
7. Re1! Kb2
8. Ra1! and we have already seen the rest of this above +-. Or
6. …..Ka3 (Kc1 7.Rxa2 wins easy)
7. Re1 with Ra1 to follow if necessary, and we have seen the rest already.
Due to length issues, I will continue in my next comment with the alternatives for black at move 5.
In the previous comment, I analyzed the following line:
1. Re4 Kb5
2. c4 Kb4 (alternatives later)
3. c5 Kb3 (alternatives later)
4. Re3 Kb2
5. Kd3
And, I think I showed conclusively that white wins after 5. …a2 6.Re2. The main problem with a2 was that it allows black to put the rook on a1 with full immunity due to the zugzwang themes that arise after white entombs the black king on a1. So, now we need to show that black can do no better than 5. …a2. Continuing from 5.Kd3 above:
5. …..a4
6. Re2! Kb3
Or [6. …Kc1 7.Ra2+-]; or [6. …Kb1 7.Kc3! Ka1 (or 7. …a2 8.Re1#) 8.Kc2 Ka2 9.Re1 d6/d5 10.c6+-]; or [6. …Ka1 7.Kc2+-]. Continuing:
7. Re1 Kb2 (Ka2 8.Kc2+-)
Here, if black plays a move like Kb4, white will simply play Rb1 followed by Kc3 and Rb4 to win: [7. …Kb4 8.Rb1 Kc5 9.Kc3 d5 10.Rb4 d4 11.Rd4 Kb5 12.Rb4 Ka5 13.Rb1+-]. Of course, if 7. …a2, white will just put the rook on a1 as we have seen previously, and wait until black is forced to make the fatal moves. Continuing from 7. …Kb2 above:
8. Kd2 Kb3 (a2 9.Ra1; Ka2 9.Kc2)
9. Rb1! Kc4 (Ka2 10.Kc2 d6 11.c6)
10.Kc2 Kc5 (what else now?)
11.Kc3 d5
12.Rb4 d4 (a2 13.Ra4+-)
13.Rd4 Kb5 (a2 14.Ra4+-)
14.Rb4 Ka5
15.Rb1+- and both pawns will fall.
So, now we need to back up to the variations at move 3 again.
1. Re4 Kb5
2. c4 Kb4 (alternatives later)
3. c5
We have, so far, covered Kxc5 and Kb3. We are left with Kb5 and Kc3:
3. …..Kb5
4. Re3 Kb4 (a2 5.Ra3 wins)
5. Kd2+-
And we have already seen this exact position in an earlier comment, but without the white c-pawn being on the board, and I showed it loses for black anyway.
And for 3. …Kc3:
3. …..Kc3
4. Re3+- and we have seen the positions that arise after Kb4, Kb2 here, and they lose, as do the trivial losing moves of Kc2, Kc4, and Kd4 (they lose to Rxa3).
Finally, we are now ready to address the options at move 2 for black:
1. Re4 Kb5
2. c4 Kc5
Prevents an immediate c5 by white, which is what he would play should black play Ka4 (we already analyzed Kb4 earlier). Also, if black plays the king to the 6th rank, white just takes at e3 with the rook followed by Ra3 or Rxa3. Continuing:
3. Re3! Kc4 (a2 and Kb4 below)
4. Ra3 Kb4
5. Rd3 a4
6. Kc2 a3 (what else?)
7. Rd7+-.
And, finally, lets back up the move 3 in this variation. For reference, this line: (1.Re4 Kb5 2.c4 Kc5 3.Re3).
3. …..a2
4. Ra3 Kc4
5. Ra2 Kb4
6. Kd3 d5
Or [6. …a4 7.Rb2 Ka3 8.Kc3+-]. Continuing:
7. Kd4 a4
8. Rb2 Ka3 (Ka5 9.Kd5 wins easy)
9. Kc3 d4
10.Kc2 d3
11.Kc3 d2
12.Rb1! Ka2 (d1Q 13.Rd1 wins easy)
13.Rd1 with mate to follow in a few more moves.
And, lastly:
3. …..Kb4
4. Kd2 d6
Variations that arise from Kxc4, a4 and a2 are fully covered in the the analyses above. Continuing:
5. Kc2 a2
Though long, simple counting shows black will lose with 5. …Kc4 as long as white isn’t too hasty in capturing at a5: [5. …Kc4 6.Ra3 Kb4 7.Rd3 Kc5 8.Kb3 d5 9.Ka4 Kc4 10.Rd1 d4 11.Rc1! Kd3 12.Ka5 Kd2 13.Rc8 d3 14.Kb4 Ke2 15.Kc3 d2 16.Re8! Kd1 17.Rd8 Ke1 18.Rxd2+-]. Also, if black plays 5. …a4, white wins with 6.Rd3. Continuing from 5. …a2 above:
6. Kb2 Kc4
7. Ka2 d5
8. Re8
I have no idea what the shortest win here is for white, but the natural looking move to me in this position is putting the rook where he can threaten the a-pawn, the d-pawn, and to check the black king all in one move- the 8th rank provides this flexibility. Continuing:
8. …..d4
It won’t matter what black does here. Most of these lines are transpositions or near transpositions. The basics here is that black simply can’t advance either pawn fast enough, and bringing the a-pawn forward just gives white an extra tempo to capture it with his king, and putting the king on the d-file at d4 or d3 will just hand another tempo to white. Continuing from 8. …d4 above:
9. Rc8 Kb4
10.Kb2 a4
11.Kc2 a3
12.Ra8 d3 (a2 13.Ra2+-)
13.Kd3 Kb3
14.Rb8 Ka4 (Ka2 15.Kc2+-)
15.Kc4 Ka5
16.Ra8+-
And, unless someone can suggest a better first move for black, I think I am done here.
One last item I want to discuss related to my very first comment and the analysis of 1.Rxe3. When I wrote out that comment yesterday afternoon, I hadn’t yet delved into 1.Re4 and, especially, I hadn’t yet envisioned the lines there where white puts the rook on a1 daring black to take it. On looking over that first comment a few minutes ago, I wondered if I had overlooked such a maneuver winning since I hadn’t even considered that possibility in 1.Rxe3 line. I don’t think white can win with it anyway, though it took me a few minutes to figure the drawing line for black:
1. Re3 Kb4
2. Kd2 a2
3. Re1 Ka3
4. c4 Kb2
5. Ra1
For all appearances, it seems this should win for white based on the analysis of the 1.Re4 variations. However, black can actually capture the rook here:
5. …..Ka1!
6. Kc2 d5
7. c5 d4
8. c6 d3
9. Kc1 d2
10.Kd2 Kb1
11.c7 a1Q and black has a draw at the very least. Though up a pawn, I doubt there is forced win here for black. Of course, the difference was having the white pawn on c4 instead of c5 as arises in the 1.Re4 variations- white is one move behind. In addition, white cannot capture at d5 on move 7 to win either:
7. cd5 a4
8. d6 a3
9. Kb3
Stalemate otherwise:
9. …..Kb1
10.d7 a1Q with, again, a draw at a minimum.
When it takes Yancey five lengthy posts to wade through the ramifications of a puzzle, I know that puzzle is completely out of my league.
Anonymous,
The length is due to my compulsive need for “conclusive proof”- plus, for me, it is a form of mental recreation. However, one could take the approach of Miguel and find the major themes involved, and be satisfied one had solved the problem. Finding those themes is pretty good proof that one could, if desired, “wade through” the variations.
1. Re4! (this gives white an extra tempo that allows him to play c5 later)
… Kb5
2. c4+ Kb4
3. c5+ Kb3 (while plays Ra4 if black takes the c pawn)
4. Re3+ Kb2
5. Kd3 a2
6. Re2+! (not Re1 as white needs to be able to play Ra1 later)
… Kb1
7. Re1+ Kb2
8. Ra1! Kxa1
9. Kc2 a4
10. Kc1 a3
11. Kc2 d5
12. c6 d4
13. c7 d3+
14. Kxd3! Kb2 (or Kb1)
15. c8=Q a1=Q
16. Qc2++ mate
I also could not solve this, but it’s fabulous and sort of simple if s.k.srivastava gave the correct line, as I guess he did:
1. Re3 Kb4
2. Rb3+ Ka4
Seems difficult for white now, but
3. Rb1!
White must already have decided to sack his rook in the corner!
3. … a2
4. Ra1 Ka3
5. Kd2!
Very neat move to avoid zugzwang being turned against white.
5. … Kb2
6. Kd1 Kxa1
7. Kc1!
Black king for ever staying in the corner!
7. … d5 (d6 or a4 turns out the same)
8. c3! a4
9. Kc2
White king between c1 and c2 as long as needed to enforce d4 by zugzwang, then cxd4 wins.
Very nice!
There must also be a line when black avoids taking white’s rook sack, but in that case white just pushes c-pawn to deflect black king, then white can slowly pick black’s pawns, staying up with a rook.
pht, unfortunately, s.k.srivastava’s line fails due to stalemate. The basic problem is that black steals a march on white right at move 7 in your line. Either white keeps his pawn on the c-file, or he captures black’s pawn at d4. If he retains the pawn on the c-file, black just pushes the d-pawn gaining a tempo while driving the king off of the c-file, or white captures at d2 again allowing the black king out of the hole, and in this case black will actually win the race.
In full:
1. Re3 Kb4
2. Rb3 Ka4
3. Rb1 a2
4. Ra1 Ka3
5. Kd2 Kb2
6. Kd1 Ka1!
7. Kc1 d5
I also think black draws with d6 and a4 here, but will leave those unanalyzed- d5 is just clear cut:
8. c3 d4 (or a4)
9. cd4
It is this or lose the game for white: [9.c4?? d3 10.c5 d2 11.Kd2 Kb2 12.c6 a1Q wins for black]. Continuing:
9. …..a4
10.d5 a3
And now white must allow stalemate since he still loses the pawn race if he allows the black king off of a1.
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