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Main variation I chose to be a fancy variation
1.Qf4+ Ke7
2.Qf7+ Kxf7
3.d8=N+ Kf6+
4.Nxb7
(4…..Kd7 5.Na5 Ke6 6.Nc4 Kd5 7.Nxa3 Kd4 8.Nc2+ Kc3 9.Kg6 (To much disappoint ment to black 9…. KxN is not viable because of 10.a4 double move by P which we forget) Kc4 10.Kf5 Kb5 11.Ke4 Kc4 12.a4 Kc5 13.Kd3 Kb6 14.Kc4 Ka5 15.Kb3 Kb6 16.Kb4 Ka6 17.Nd4 Kb7 18.Kb5 Ka7 19.a5 Kb7 20.a6+ Ka7 21.Ne6 Ka8 22.Kb6 Kb8 23.a7+ Kc8 24.a8=Q+ wins)
4…. Ke5
5.Kg6 Kd4
6.Kf5 Kc3
7.Ke4 Kb2
8.Kd3 Kxa2
9.Kc2 Ka1
10.Nc5 Ka2
11.Nd3 Ka1
12.Nc1 a2
13.Nb3# There may be so many alternatives at every move but the character remains unchanged.
1. Qf4+ (Ke7 or Ke6)
2. Qf7+ (if Black’s King captures the white Queen then d8=knight!, check and will eventually take the black Queen, soon, the Knight then can take the black pawn and will be able to protect the remaining white pawn)
Now, if after 2. Qf7 is answered by either Kd6 or Kd5, then white can simply answer it by 3. D8=knight!
“scrabble”
Not surprisingly, this puzzle seems at first impossible.
It looks like if I start with check (alas not possible from g7/f7/e7 here), it would go:
1. Qh4+ (to prevent Ke7) Ke6!
2. Qf4+ (enforsed against Kxd7) Kd6!
3. Qd4+ (again enforced) Ke6 and this will be draw by repetition.
So it looks like it’s impossible to keep d7 pawn without drawing, and it’s also unlikely to get better than a draw without that pawn, even if I’m up with the a2 pawn.
So I must come up with something spectacular. Probably a sack.
The idea Qa6+?/Qc6+? can quickly be excluded.
It strikes me that a knight could be involved here!
If I’m able to sack my Q on f7 that looks at least interesting.
So I try:
1. Qf4+ Ke7
2. Qf7+ Kxf7 (Kd8?? Qe8+ mates or Kd6?? d8=Q+)
3. d8=N+ Ke7
4. Nxb7 Kd7
But alas, it’s still far from obvious how white wins. White king is too far away. I guess I simply found one of the plans that don’t work….
ht
I guess I had a really interesting idea here:
1. Qf4+ Ke7
2. Qf7+ Kxf7
3. d8=S+
From here there seems to be 2 lines:
A)
3. … Kf6+
4. Nxb7
and black K goes hunting a2 and takes it too. White king simply follows and succeeds trapping black king behind his own pawn with Kc2.
Only then knight starts moving, king stays on c2. In the end black might be elegantly mated in the corner after Ka1 Nc1! (zugzwang) a2 Nb3#.
B)
3. … Ke7
4. Nxb7 Kd7
Here black has determined for the time being NOT to take the a2 pawn, but instead wants to irritate that knight as much as possible. And perhaps manage to trade off pawns.
But this seems perhaps to go:
5. Na5 Kd6
6. Nd4+ Kc5
7. Nxa3 Kb4
8. Nb1!
From here it seems black king can’t do anything (can reach d3 but NOT c2), now white king starts walking and will reach b2 (via first rank), and then the endgame must be won for white.
But this line at least lasts longer than A…
[…]
3. d8=N
[…]
mhm, no… it doesn’t work; it is a good threat though, in many lines.
1. Qf4+ .. Ke6
2. Qg4+ .. Kd6 or the black queen is skewered or Qg7+ is allowed
3. Qe4+ ..
I don’t know…
Happy new year!
One thing I have gained from the constant practice of trying to solve these problems over the years is to ask myself why pieces are where they are- composers of problems design these things with deliberation, after all! The queen on b7 is one of those items- why is she there? The answer occurred to me almost instantly- we were looking for an underpromotion to a knight. This is even more effective an idea if black can be induced to put the king on f7! The first move is the most logical beginning:
1. Qf4
There are other checks here, and there are other starting moves, but this move was “obvious” to me since I could play a subsequent 2.Qf7 offering the queen sacrifice for my desired position. Let’s just have black cooperate for a moment:
1. ……Ke7/e6 (more here later)
2. Qf7 Kf7
3. d8N Kf6
4. Nb7
Now, it may appear that this is clearly won for white- his knight will go down and capture a3, and then protect the white pawn from b1 as the white pawn is pushed carefully to a3- preventing black from capturing the the knight. However, this is where I found the real issue- I couldn’t make that plan work:
4. ……Ke5 (going for the pawns)
5. Na5 Kd4
And the white knight is cut off from c4- the square from which to win a3. The white knight can protect the white pawn from b4, but the black king can shuffle from c3 to b2 forcing the white knight away and back again just to hold the pawn- the white king will never get a chance to make a move before losing either the pawn or the knight.
So, I had to ask myself- was I wrong right from the start, or is there a way to actually win this ending. The only real chance I could see was to move the white king at move 5. Let’s take the proposed line from the top:
1. Qf4 Ke6
2. Qf7 Kf7
3. d8Q Kf6
4. Nb7 Ke5
5. Kg6
My idea was to get the king in the game earlier to protect the knight at b4 while it protects the pawn, but I realized at move 6 what the real final theme was going to be, and I was lucky in that I had seen similar endings in composed problems in the past- Susan has posted number of these over the years. The black king will be mated on a1 with his pawn on b2- the white pawn will sacrificed to draw the black king into the trap. The only question in my mind was just how to accomplish this. Let’s continue, though I haven’t yet really looked for holes in the entire plan:
5. ……Kd4 (still going for a2)
6. Kf5 Kc3
7. Ke4 Kb2
Now, at this point, I am absolutely certain that black is making the least resistant move- it is probably better to play a move like 7. …Kc4 here, but I just want to illustrate the danger black is in:
8. Kd3 Ka2
9. Kc2
Now it is all forced:
9. ……Ka1
10.Nc5 Ka2 (a2 11.Nb3#)
11.Nd3 Ka1
12.Nc1 a2
13.Nb3#
Now, obviously, I have left a ton of options out for black here, and I hope to foreclose all of them at a later point today, but I first want to return to the very beginning of this puzzle- can black avoid putting that king on f7 allowing the knight fork? No, he can’t- that I can foreclose. Let’s start over:
1. Qf4 Ke6
2. Qf7 Ke5 (Kd6 3.d8Q with check!)
3. Qe7 Kany
And now white will queen the queen the pawn and the queens protect each other. That ending is trivial to win. And….
1. ……Ke7
2. Qf7 Kd8
3. Qe8 Kc7
4. d8Q#
Later today I will consider some of blacks alternatives once the queens are off the boards- when I have worked them out to my satisfaction.
This is one of the great compositions I’ve seen. I was logging in to post that the main idea seems to be to sac the Q on f7, underpromote to s N forking K and Q, and then chase black’s K to a2 and put the W K on c2 to keep him there, then mate with Nc5-d3-c1-b3. The timing is right for this since with the W K on c2 and Black K on a2, with black to move, …Ka1 Nc5 a2 Nb3 is mate and …Ka1 Nc5 Ka2 Nd3 Ka1 Nc1 allows only ….a2 Nb3#.
And I find that Professor Bhat has posted it already. A very pretty combination of ideas. Well done, Professsor!
A small comment to Prof. Bath’s main line:
7.Ke4 Kb2
8.Kd3 Kxa2
It looked so obvious with 8. … Kxa2, but what if black is funny and instead plays:
8. … Ka1
I guess we all see that in this case 9. Kc2? would be an error leading to draw, because of 9. … Kxa2 with zugzwang bringing knight to a black field, which is wrong when black king is on white field!
So instead:
9. Kc3! Kxa2 (otherwise Kb3 and Kxa3 etc.)
10. Kc2!
So there is something to be careful about here, but not much:-)
I am trying to find out some clarity through the maze of complications. If black K goes after WP white K should immediately follow and inflict smothered mate at a1. So I did not seek all possible options in this case. The second black K does not go at WP but helds on to a8 to b8. The question here is whether tempo is required here or not.
Assume white K at b6,P at a6 and N somewhere else.Obviously white K is tied.He can not gain a tempo.We certainly know N can not gain a tempo.wherever N is there it is to be brought to c7.If black K is at a8 it is a check and has to move to b8.Now white plays a7+ and black can not revert to a8.Instead suppose black K were at b8 .Then Nc7 is not a check but black K at b8 can not go to a8 but go to c8 and white P queens.It was a blow to my embedded concept of tempo requirement for N.I think once these are clear the puzzle is a peanut.I only had trouble when white K delayed following and N had to support P from b4 when black K reached b2 but had to go away when black K played Kc3 resulting in repetetion of moves.
Professor Bhat,
Yes, the pawn ending is won regardless of where the pieces start- white has waiting moves with both the knight and king. The tempi you talk about, however, are very important in regards to the smothered mate at a1. I will show you a variation below that demonstrates this.
As for the composition, you were right- most of the variations are not of changed character- all white needs to do is to stay within distance enough to make sure to trap the black king in front of his pawn if he captures at a2, and with the proper orientation. The only other major variation is where black neither proceeds to capture at a2, but continues to deny the knight access to c4. For example, the following line. And I will use it to illustrate something that got passed over in the comments from yesterday- that smothered mate is more technical than it appears.
1. Qf4 Ke6
2. Qf7 Kf7
3. d8N Kf6
4. Nb7 Ke5
5. Kg6 Kd4
6. Kf5 Kc3
7. Ke4 Kc4
The variation I mentioned in my comment that offers more resistance than proceeding with 7. …Kb2. From this point, the most logical way to win is to first threaten to take away the c3 square from black:
8. Ke3 Kc3 (else 9.Kd2+-)
Now, white brings the knight into the game to force black to make a decision:
9. Nc5 Kb4
Black’s other options are no better. He can’t play to b2 and then a2 since the white king stands ready to trap him on the a-file with Kd2 and Kc2/c1. And if he plays Kc2, white just takes c3 away with a move like Ne4 or Na4 (see below). Continuing:
10.Kd4
The most direct plan. Guard the knight and take control of c3. Now the a-pawn falls since black must keep giving way. Now, lets finish off with 9. …Kc2:
9. ……Kc2
10.Ne4
Here, white must avoid the pitfall- 10.Kd4?- a move that allows black to escape with the draw. In that variation, black can capture the a2 pawn, and while white can still trap the black king on the a-file, it is impossible to mate him now without cooperation from black. The details are left for your amusement. Continuing from 10.Ne4 above:
10. …..Kc1 (Kd1 11.Nc3)
11.Kd3 Kb1/b2
Of course, it more resistant (in terms of total moves) to play a move like Kd1 here, forcing white to capture at a3 and queen the pawn, however, the critical conceptual lines are these. Continuing:
12.Kd2
The easiest of the moves work with. Like I wrote above- it isn’t only critical to trap the black king on the a-file, but white must have the proper orientation of his knight and king in order to avoid stalemates when doing so. From d2, the white king stands ready to trap from both c1 and c2. The easiest way to think about it is this- white needs to be ready to mate on the move immediately after black plays a2. Because of its nature, the knight cannot make waiting moves once it is in that mating pose- only the king can do that. So, now, all of black’s options lead to mate:
12. …..Kb1 (Ka2 13.Kc2!;Ka1 13.Kc1)
13.Nc5
The shortest of the mates, I think. To play other moves, white will end up repeating one or more of them to enforce the mate. Continuing:
13. …..Kb2 (Ka1 14.Kc2;Ka2 14.Kc1!)
Note the difference of white’s replies after Kxa2 in the last two parenthetical variations. The difference is where the knight stands- in one, white can only win with Kc2, while Kc1 is the winning move in the other. Continuing:
14.Nd3
Taking the b2 square away, now. Continuing:
14. …..Kb1 (Ka1 15.Kc2;Ka2 15.Kc2!)
15.Kc3
Here, white will win with Kd1, and in the same number of moves, I think. If black captures at a2 now, white traps properly with Kc2, so Kc3 here is ok now. In any case, the longest resistance for black is…
15. …..Ka1
16.Kc2 Ka2 (finally forced into it)
17.Nb4!
The only winning move. Continuing:
17. …..Ka1
18.Kc1!
The only winning move. Continuing:
18. …..a2
19.Nc2#
Prof Bhat,
Thanks for highlighting the issue of tempo requirement in case BK abandons the a pawn and takes refuge at a/b8. Honestly I did not have an opportunity to see this problem. However, I now have!
To me the winning position is WP at a6 and WN at c5. The WK can be anywhere. This is easy to achieve where BK can attack neither the pawn (as Wn protects it) nor capture the WN as the WP at a6 would Queen! BK can only mark time at a7,a8,b8!
The WK can saunter across from anywhere on the Board to a5,b5. The objective is for the WK to reach b6 which it can do easily by losing a tempi on a5/b5/c6 to ensure that BK vacates a7!
Now irrespective of where BK lands up, W wins with
A- if BK is on a8 – by Ne5, a7+ and Nc7! Or
B- if BK is on b8 – by Ne5, Ne7+ and a7+
In essence, W can create the tempo he wants with WK with an a pawn and WN even though the WN cannot lose/gain a tempo! This applies to a h pawn as well!
But W cannot create the tempo he wants with the WK with an a pawn and a black colored WB even though the WB can lose/gain a tempo!
Strange but true!
Harry,
Regarding your reference to dark_square WB even though it can gain/lose tempo (or can make waiting moves)it can never control a8 which is the root problem. With WN however I had wrong preconceived idea that BK must be at certain place only for winning.Obviously WK at b6,pawn at a7 and N elsewhere no waiting move is possible.N can be siad to have made waiting move if it comes back to its original position after 3 moves.This is impossible.WK at b6 has also lost capability of making waiting moves since if he chooses a5,b5 and b6 for this he has to give square a7 to black and black K has also got 3 squares a7,a8 and b8.I was shocked to know that there is no problem of waiting move at all.It is a relief that BK at either a8 or b8 is o.k. WN may be miles away but can be brought to c7 at leisure in care free manner.But a prmature push a7 without N being ready to deliver mate at a8 can lead to stalemate.But as Yancey pointed out black’s dilly-dallying policy of capturing or not capturing WP has do be handled carefully.
Prof.Bhat,
I agree. The key is to have WP at a6 and WN at c5 as I pointed in my second para. WP at a7 does not work and will lead to stalemate as b8 is no longer available for BK or lead to loss of a7 WP if W loses control of a7.
The point I wanted to make was that it is surprising that a N that cannot lose a tempo allows WK to lose/ gain a tempo whereas a B that can gain/ lose tempo does not allow the WK gain/lose a tempo so to speak!