White to move. How should White proceed?
4k2r/4p2p/1p2n1pb/1NpQp3/4B2P/2P3P1/p2P1PK1/2q2n2 w k – 0 1
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The most obvious move is 1.Qe6, but I don’t see much but defeat after black takes at d2:
1. Qe6 Qd2
And now what? Qc8 is no threat:
2. Qc8 Kf7 and it is over. Or
2. Bc6 Kf8 and black hides at g7, eventually. Or
2. Nc7 Kf8 again. Or
2. Bd5 Ne3
3. Kh3 Qd5 wins easily for black.
1.Nd6+! Kd8 (…Kd7 2.Qc6+! and mate) 2.Qa8+ Kd7 3.Qc6+! and 4.Qc8 mate
or 1…exd6 2.Qxe6+ Kd8 3.Bc6!+-
or 1…Kf8 2.Qxe6 exd6 3.Qf6+ Ke8 4.Bc6 mate or 3…Kg8 4.Bd5 mate
This is called a modifying sacrifice ! and it’s a very nice one
The next most obvious move to me is
1. Nd6. This has the advantage over the previous line in that it if black takes at d6, the black king no longer has the e7 pawn to hide behind, and white takes at e6 with check. There are two major lines I see:
1. Nd6 Kf8??
2. Qe6 ed6 (otherwise Qf7#)
3. Qf6 Kg8 (Ke8 4. Bc6#)
4. Bd5# Better for black is to just take at d6 in the first place:
1. Nd6 ed6
2. Qe6 Kd8 (Kf8 3.Qf6+- see above)
And, here, it diverges on two paths. Initially, I preferred
3. Qd6 Ke8 (Kc8 see below)
4. Bc6 Kf7
5. Qd7 Kf6 (Kf8 or Kg8 is mate)
6. Bd5 and there is nothing but sacrificial delaying moves that prevent Qf7 or Qe6. However, at move 3 above, black could play
3…….Kc8
and, here, I thought that Bc6 would be a forced win, but then I saw
4. Bc6 Qd2!!
5. Qe6 Kc7!(Kb8 allows perpetual)
and I see no way to hold this for white- the attack on the bishop must be addressed, and black is threatening Ne3, too. Alternatively, at move 4, white could try
4. Qe6 Kd8 and this looks like a draw to me. A draw might be all white gets anyway, but no harm in looking at the other plan for white at move 3- there are, now that I am looking at it again, two (I overlooked this one below, and was very excited, at first, as it solved the problem of Qd2 I noted above, however, working through it, I found a very clever defense for black):
1. Nd6 ed6
2. Qe6 Kd8
3. Bc6 Nf3 (nothing else)
4. de3 Qf1
5. Kf1
This is forced as Kh3 loses to Qf2 (the queens get exchanged by a later Qf5+ or white is mated by a1(Q)), and Kf3 loses to Qh1+. Continuing:
5. …..a1(Q)
6. Kg2 Qa7
7. Qd6 Kc8
8. Qe6 Kd8 (Kb8 9.Qe5)
9. Qf6 Qe7 (Kc7 10.Qe7)
10.Qh8 Bf8,
And here, I just don’t know. I think black has parried the major threats. He is down a pawn, but I don’t know if it is enough to win for white. Someone might want to stick it into a chess engine and let me know what it says.
The last plan for white that I see is:
1. Nd6 ed6
2. Qe6 Kd8
3. Qf6 Kd7
4. Qh8 a1(Q) (what else?)
5. Qh7 and I don’t see anything more than a perpetual check here.
My head is hurting. If there is a win for white, I am missing it. I can draw the position, and, maybe force a win in one of the lines above, but I am missing a clear and force line if there is one.
1. Nd6+ exd6
(1.. Kf8 2. Qxe6 is the same line,
1.. Kd8 2. Qa8+ Kd7 3. Qc6+ Kd8
4. Qc8#)
2. Qxe6+ Kd8 (2.. Kf8 3. Bd5 1-0)
3. Bc6 Kc7
4. Qd7+ Kb8
5. Qb7#
Nd6+ exd6 Qxe6+ Kf8 or Kd8 the bishop then targets the square in front of the king and the queen mates the next moves. Since black needs two moves for mate and gets only one that should suffice. The king moving instead of exd6 shouldn’t change the outcome at all.
1.Qxe6 a1(Q) 2. Nd6+ Kd8 (if 2…Kf8 3.Qf7 mate) 3.Qc8 mate.
Kamalakanta
1. Qxe6 Qxd2 …
1. Qxe6 Qxd2
prevents Nd6 check
How about?
Line 1
1. Nd6+
1. …..exd6
2. Qxe6+ Kf8
3. Bd5 (Mate next move with Qf7++)
Line 2
1. Nd6+
1. …..exd6
2. Qxe6+ Kd8
3. Bc6 (Mate next move with Qd7++)
Line 3
1. Nd6+
1. …..Kf8
2. Qf7#
Line 4
1. Nd6+
1. …..Kd8
2. Qxe6 Kc7
3. Qxe7+ Kb8
4. Qb7#
Line 5
1. Nd6+
1. …..Kd7
2. Qc6#
I think Qxe6 will be refuted by Qxe2.
Best is 1. Nd6+!!, now if 1… Kd7 then 2. Qc6+ Kd8 3. Qc8+ mate, and if 1… Kf8 2. Qxe6 (threatening mate on f7) 2… exd6 Qf6+ and mates next move.
Rajesh and Timothy,
What about
1. Nd6 ed6
2. Qe6 Kd8
3. Bc6 Ne3 white must take or draw
4. de3 Qf1 white must take or lose
5. Kf1 a1(Q)
6. Kg2 Qa7 stops the immediate mate threat. I don’t remember looking at this earlier, but I must have and dismissed it as an interpolation of a line I did analyze in my comment above. Again, if there is a clear win for white here, I am missing it.
Don’t know
1. Qe6 with the threat of Nd6
1…Kd8 2. Bc6 and wins!
Ok, I came at this with a fresh brain this morning, and I think I have it solved, but it is complicated by the variation numbers, and I might still be missing a way out for black. A number of the lines collapse into each other, but I can’t always be certain which ones. I was close yesterday at the end, but missed the correct continuations in my agitation.
1. Nd6 ed6
2. Qe6 Kd8
3. Qf6! Kc8(see alternatives below)
4. Qh8 Kd7(Kc7 same, I think)
5. Qh7 Ke6(see alternatives below)
6. Bg6! Ne3(d5, see below)
7. de3 Qf1
8. Kf1 a1(Q)
9. Kg2 Qa8
10.e4 d5 (Qf8 11.Bf5 wins queen)
11.Bf5 Kf6(Kd6 12.Qd7#)
12.Qh6 is a won endgame, but 12.g4!! is a very, very pretty mating attack I will leave as an exercise, or a problem if Susan wants to post it.
At move 6 above, rather than sacrificing the knight and the queen to get the new queen back for the defense of the black king, black could have played
6. …..d5
7. Bf5 Kf6 (Kd6 8.Qd7#)
8. Qh6! Kf5 (Kf7 doesn’t help)
9. g4 Ke4 (Kg4 10.Qg5#)
10.Qg6 Kf4
11.Qf5#
At move 8 above, Kf7 won’t help as the king is helpless against the queen and bishop all by himself- the actual mates are left as an excercise.
At move 5 above, black had the option of returning to the back rank rather than getting caught at e6. There were Kc8, Kd8, and Ke8:
5. …..Ke8
6. Bc6 Kf8
7. Qh6 and there almost certainly a forced mate here, but even if not, black will be forced to give up the knight in order to bring a queen back for the defense, and white should easily win the resulting Queen and pawn vs Queen, Bishop and pawn endgame. Also,
5. …..Kd8
6. Bc6 and there is no way to prevent mate other than delaying moves like Bg7, or the sacrificial line starting with Ne3- the new queen can’t reach a7 in this position. Finally
5. …..Kc8
6. Qb7 Kd8
7. Bc6 also mates after the delaying moves are played out.
At move 4 above black could have played
4. …..Kc7
5. Qh8 and this looks just like the variation from move 5 above.
At move 3 above, black had the other options of Kc7, Kd7, and Ke8 rather than Kc8:
3. …..Ke8
4. Bc6#
Or
3. …..Kd7
4. Qf7 Kd8 (Kc8 5.Qb7 Kd8 6.Bc6+-)
5. Bc6 and mate can’t be prevented since a7 is unavailable to the queen that arises in the 5. …Ne3 line. And finally, at last,
3. …..Kc7
4. Qe7 Kc8
5. Qb7 Kd8
6. Bc6 wins just like above.
Phew. Good practice working through all of this. I can do about 5 moves deep in my head, but detailed analysis like this requires my chessboard. If I have overlooked anything (easy to do), that invalidates the above, let me know and I will see if I can find a work around.
1.Nd6+!
A)
now if
1…PxN
2.QxN+ Kf8
3.Bd5
threatening Qf7 mate and black can do nothing about it.
if 2…Kd8
3.Bc6
threatening Qd2 mate.
if 3…Kc7
4.Qd7+ Kb8
5.Qb7#
B) if
1…Kf8
2.QxN threatening Qf7 mate
2…PxN
3.Bd5
C) if
1…Kd8
2.QxN threatening Qc8 mate.
2…PxN
3.Bc6