Wednesday, July 30, 2014

Checkmate in 6

White to move and checkmate in 6.

8/2p5/p7/2p5/kNK5/p7/P7/8 w - - 0 1

Dziewonski, 1855


sivip said...

Nice and completly forced:
1.Nc6 a5 2.Na7 c6 3.Nb5 cxb5+ 4.Kxc5 b4 5.Kc4 b3 6.axb3+

pht said...

I rather early found 1. Kxc5 to be the best looking move.

1. Kxc5 Ka5 (looks best)
2. Nc6+!

It took it's time to find out that this works, since I had started out with excluding the Nc6 move for being stalemating...

2. ... Ka4
3. Kc4! (nice zugzwang) a5 (only move now, both Ka5 and c6 prevented by the knight)
4. Nd4/Ne5 c6
5. Ne2/Nd3 c5
6. Nc3#/Nxc5#

Alternatives on first move:

1. ... a5?
2. Nd5! c6 (only)
3. Nb6#/Nc3#

1. ... c6
2. Nd3! (enforced) Ka5 (2. ... a5 3. Kc4! c5 4. Nxc5# was an important sideline)

Here Nd3 nicely prevents Kb4, allowing white king to do a job on c6 and b6.

3. Kxc6 Ka4 (only)
4. Kb6! a5 (only)
5. Nc5#

Line B here was the one I first saw.
The big problem was when black insisted on repeating with Ka5 and Ka4 and c7 prevented white from playing Kb6.

Therefore after 1. ... Ka5 I had to switch idea completely and play 2. Nc6+ (active knight) instead of 2. Nd3 (active king).

Harry Hariharan said...

One of the toughest problems becuse 6 moves is really a challenge.
In the first round of trials I got mates ranging between 2 and 7 moves, ie., 7 moves generally but there were some variations which took 11 moves.
Finally, I got the solution!
1. Kxc5!!
>>B2-2...Ka5.3.Nc1.Ka4.4.Nb3.a5. 5.Kc4.c5.6.Nxc5#
>>C1-2...c6.3.Nc1.Ka4.4.Nb3.a5. 5.Kc4.c5.6.Nxc5#
>>>C23-3...Ka5.4.Nb3+.Ka4.5.Kc4.c5. 6.Nxc5#.Ka5.7.Nd7.Ka4.8.Kc5.Ka5. 9.Ne5.Ka4.10.Nc4.a5.11.Nb6#

The only problem I have is that the last variation C23 is a 11 move mate. This I will try to crack. Has anybody else cracked this?


Yancey Ward said...

As it turns out, this isn't a difficult problem given the mostly forced nature of the solution from the black side.

I could quickly and easily visualize two different mating patterns here, though not quite how to reach them immediately. The first is forcing the black to play a5 with the king on a4, and then mating the immobilized king from either b6, c5, or c3 with the knight. The other is to force the same immobilization, then give up the knight at b5 and then force black to play a pawn to b3 at which time axb3 will provide the mate. While I think I can mate with either of these ideas, the former seems to be at least 11 moves if my work is correct. However, the first move of the second possible solution here is a bit obvious in that it is the move that most quickly forces black to play a5, and the rest is utterly forced:

1. Nc6 a5 (only legal move)
2. Na7!

The hardest part of this problem. Any knight move forces c6, however, if white takes at c5, black is stalemated, and white cannot open the b5 square for black. Given that I had already considered the idea of mating with a pawn move, it was easy to just continue with the only move that allows a knight sacrifice on the b-file on the next move. The rest is forced:

2. .....c6 (only legal move)
3. Nb5!

White can probably win with a move like Kc3 here, but I am not sure of it having not analyzed it to the end: [3.Kc3?! c4 4.Nc6 Kb5 5.Ne5 should be winning]. Continuing:

3. .....cb5 (only legal move)
4. Kc5 b4 (only legal move)
5. Kc4 b3 (only legal move)
6. ab3#

Anonymous said...

Nc6 a5
Na7 c6
Nb5 cb5
Kc5 b4
Kc4 b3
ab3 mate!

PROF.S.G.BHAT said...

Very hard.Knight can not gain a tempo but black has a choice of ...b6 and ...b5 or directly ....b5.
I was trying for N at b3 being captured by black's P and axb3 but such a position never arose.Then I tried giving up N early and trying for axPb3. After 3 hours of dilly dallying I got it.
1.Nc6 a5
2.Na7 c6
3.Nb5 cxb5+
4.Kxc5 b4
5.Kc4 b3

pht said...

Wow, the line starting with Nc6 is undoubtedly correct, and very elegant!

Zugzwang on 6 moves on a row is really special!

But hard to find though.

I notice that only I and Harry had a more "human" solution here (with many lines)
I even managed to keep it within 6 moves in all lines, but I must probably have missed something then?
Or are there 2 solutions?

My line was:

1. Kxc5 Ka5

Alternative moves seem to loose quicker, but did I miss something on 1. ... a5/c6?

2. Nc6+!

Here Harry's idea 2. Nd3 was wrong.

By playing Nc6 here (one move delayed) a actually get into a zugzwang sequence a bit similar to the main line, but without sacking knight....

2. ... Ka4 (only move)
3. Kc4! a5 (only move)
4. Nd4/Ne5 c6 (only move)
5. Ne2/Nd3/Nd7 c5 (only move)
6. Nc3#/Nxc5#

PROF.S.G.BHAT said...

Dear Yancey, 3.Kc3 will not work because there are only two pieces for white K and N.N can not gain a tempo,King can not have triangulation as black k would escape. so without analyzing any thing i can say there is only one solution.

Yancey Ward said...

Prof SG Bhat,

White can win the endgame in that line, I think. Will look it up in a Nalimov tablebase to be sure.

Yancey Ward said...


Ok, I think maybe you meant it isn't a solution, which of course it isn't. I was just pointing out that the white position is winning after 3.Kc3, not that it mates in 6- I was content to let the black king escape in that case, and just demonstrate that white can win all three black pawns while retaining his, which he can very easily.