White to move. Is this a win or draw? How should white proceed?
4k3/4P3/5K2/8/8/8/3N4/3b4 w – – 0 1
Kosek, 1912
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1Ne4 Bh5
2Ke6 Bg4+
3Kd6 now
(a) 3… Bh5
4Nf6+ kf7
5 e8=Q
(b)3…. Bd7
4 Nf6+ Kf7
5 Kxd7 wins
OR
1 Ne4 Kd7
2 Nc5+ Ke8
3 Ne6 Kd7
4 Ng7 wins
To win, white must check the black king out of e8. So, the knight needs to come to either c7, d6, or g7. To keep this knight check from winning immediately for white, black must have the bishop on either the a4/e8 diagonal or the h5/e8 diagonal when this check is delivered. Let’s look at the two most direct approaches for the knight travel plan (though, this being a chess composition, I suspect the only winning move is going to be a very indirect path starting with either Nb1 or Nf1 :~).
1. Nc4 Ba4
2. Nd6 Kd7 (only move)
3. e8(Q)
So, that part was easy. Obviously, the bishop can’t be on the a4/e8 diagonal since the black king has only one path out of e8 and blocks the cover on e8. Let’s look at the first move alternative for black in this line:
1. …..Bh5
So, now, white doesn’t seem to have a king move that doesn’t drop the pawn or the knight. A knight move like Nb6 will force black to move the bishop, but I don’t see how this is going to help- black can just play the bishop to g6 and it can’t be taken without giving up the pawn. In fact, I am pretty sure this is drawn. There is no square for the knight to drive the bishop away from the diagonal, and still threaten the check on the next move. I can see only two possible plans- a double attack from g7, or protect the pawn from b1/c6, but neither is going to work:
2. Nb6 Bg6
Here, black can give up the diagonal, I suppose, since white isn’t immediately threatening a knight check. The only move I would avoid here is Bf7: [2. …Bf7? 3.Na8! Bh5 4.Ke6! Bg4 (4. …Bf7 5.Kd6 with the unstoppable threat of Nc7+ followed by e8Q) 5.Kd6 Bd7 (5. …Kf7 6.Nc7 wins) 6.Nc7 Kf7 7.Kd7+-]. However, I can now see the winning move at move 1- the subvariation above contains a similar motif to the winning line. Let’s finish this before moving on. Continuing:
3. Nd5
To keep the guard on the pawn, while maintaining the threat of check on the next move. Continuing:
3. …..Bh5 (the only move)
4. Nf4
Of course, Nc7+ leads nowhere after Kd7. Continuing:
4. …..Bg4
I think Bf7 is ok now, but I am sure of Bg4. However, a move like Bf3 is losing: [4. …Bf3? 5.Ne6 Bh5 (5. …Bc6 6.Nc7 Kd7 7.e8Q; or 5. …Kd7 6.Ng7) 6.Ng7+-]. With 4. …Bg4, black can take at e6 if white plays 5.Ne6 since the recapture with Ke6 is a stalemate.
Try as I might, I can’t make 1.Nc4 work in any variation. However, one of the subvariations in which white creates a mating threat with the white king at e6 above got me to see something I had missed from the start. Continued in my next comment.
In my last comment, I covered the line starting with 1. Nc4. In it, black was forced to play Bh5 to hold the draw, and no knight maneuver could, after the first move, force black to give up the diagonal in time for white to deliver the knight check followed by queening the pawn. However, one of the subvariations I discussed let me see why 1.Ne4 will work:
1. Ne4!
Again, the threat is 2.Nd6 followed by queening the pawn. As before, Ba4 will lose since the king will have to vacate through d7 and the pawn will queen. So, black must still try Bh5, but now this clearly loses:
1. …..Bh5
2. Ke6!
The line before failed because white is one move too late the entire way- the knight was always in the wrong place. Now black is toast- he must address the mate threat by checking the white king, but he can’t cover the other threat- a check driving the black king out through f7 at the same time:
2. …..Bg4
Here, Bf7 loses too: [2. …Bf7 3.Kd6 and there is no answer for 3.Nf6+]. Continuing:
3. Kd6 Kf7 (Bh5 4.Nf6+-)
4. Nf6 and the pawn will queen.
ne4 bh5
nd6+ kd7
nf5
1-0 black is in zugzwang and white’s next move will be Ng7
I must be missing something, because it seems fairly simple. White wants to check when the bishop is not guarding e8. So
1. Ne4 with the threat of Nd6+, and Black has only two real possibilities.
1. … Kd7
Planning 2. Nd6 Bh5 3.Nf7 Ke8.
2. Nc5+ Ke8 forced
3. Ne6
and there is no defense to 4. Ng7. Since the Black King will have to go to d7, the Bishop must guard the e8 square from h5 and will be captured by the Knight.
So let’s try
1. Ne4 Bh5
2. Ke6 Bg4+
Or 2. … Bf7+ 3. Kd6 Bg6 4. Nf6+ Kf7 and the Black King blocks the Bishop from guarding e8.
3. Kd6 Kf7 or … Bh5 or … Bd7)
4. Nf6 wins.
Am I missing something simple?
Beautiful 5-men study by Kosek, and it is sound. No cooks, no busts, and just two lines,
A delight!
I bet that Yancey Ward has solved it now!
You would win that bet, though I did get sidetracked by the invalid line.
1. Ne4 Bh5
2. Ke6 Bg4
3. Kd6 Kf7
4. Nf6
Simple but relevant. Essentially there is no easy way that the White Knight can prevent the Bishop geting onto a diagonal that will control the square e8. However, looking at it further there is a Knight threat of mate. These two factors combine for White to quickly and easily win.
1. Ne4 (obvious allowing a later Nf6 or Nd6 depending on responses). Bh5
2. Ke6 (threatening mate) Bf7+ (Bg4+ fails to 3. Kd6 Bh5, 4. Nf6) 3. Kd6 Bg6 or elsewhere 4. Nf6+ Kf7 5. e8=Q= K*f6 and white mates in a few moves.
The other line is quicker.
1. Ne4 Ba42
2. Nd6+ Kd7
3. e8=Q+ K*d6
4. e8*a4.
Psyche/ anonymous
I don’t have the exact line, but I’m sure it’s a win. The bishop can protect the queening square by going to h5, and the knight would cause a fork of the king and bishop if it gets to f6. Also, the knight on f6 would be mate if the king is on e6.
So I suggest moving the knight to e4, and this will force the bishop to h5. Then threaten mate with Ke6, forcing a check to avoid mate with Bg4+, and now move the king to d6 leaving f6 open for the knight, so that black gets forked if the bishop goes back to h5 to cover the queening square.
1.Ne4 Kd7
2.Nc5 Ke8 (if black king moves away from e8 here, white simply promotes the pawn and wins)
3.Ne6 and white will win by playing his knight to g7 in the following move since if black’s bishop now moves to h5, there will be a fork. If bishop doesn’t move on to h5, it cannot cover e8 and king will have to move away allowing white to promote his pawn. Let’s see if black can do any different at move 1.
1.Ne4 Bh5 (if bishop moves to any other square now, white simple wins as foolows –
1….Bc2
2.Nd6+ Kd7
3.e8Q+)
2.Nd6+ Kd7
3.Nf5 and black is in zugzwang. This is an easy win for white from here. But I think I am missing the best defense for black. Awaiting others’ comments.
1.Ne4
if 1. .. Ba4
2. Nd6+ Kd7
3. e8Q+
if 1. .. Bh5
2. Ke6 and black must check or Nd6#
so
2. .. Bf7+ or Bg4+
3. Kd6
and black cant avoid Nf6+, and e8Q
Hi Susan Polgar,
Well,undoubtedly piece positions favors White’s win.
In fact,to solve this puzzle none needs to dive just surface peddling would show that the white piece wins the game in style.
so I chose to give the simplest combination( simplest not in number of moves but simplest in tactics)as an example moves supporting my above comments.
White wins the game
===================
1.Nc4 Ba4
2.Nd6+ Kd7
3.e8(Q)+ K*Nd6
4.Q*Ba4 Kd5
5.Qb4 Kc6
6.Qa5 Kd6
7.Qb5 Kc7
8.Ke6 Kd8
9.Qb7 Ke8
10.Qe7++ Mate
White wins the game
By
Venky [ India – Chennai ]
1Ne4 KD7.2 Nc5 Ke83.Ne6 finito
1ne4 Bh52.Ke6 Bg4 3.Kd6 Kf74Nf6
Bf73.Kd6 then Nf6
1. Ne4 – Bh5
2. Ke6! and now after Bg4+ or Bf7+, white simply plays Kd6 and Nf6 and the e-pawn cannot be stopped.
The invalid line being
1.Ne4/c4 Kd7
2.Nd6 Bh5
3.Nf5 Be8
4.Ng6 Bg6! =
by any chance?
That was one of my 1st attempts before finding the right approach. It’s a very pretty drawing line I think.