Black threatens 56... Qxf2+ 57.Kh1 Qg2# and Rxa5.

With such threat there are only three possible moves: 56.Ng5+, 56.Rxf7+ and 56.Nd2.

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White can clear the f-file with tempo and try to protect f2 with 56.Ng5+:

A) 56... hxg5 57.Rxf7+

A.1) 57... Kg8 58.Rxf6 Kg7 (due to Qxd5+ and Qb8+) 59.Rf3 with an extra pawn and a won position. For example, 58... Rxa5 59.Qb7+ Kh6 (59... Kg8 60.Qf7+ Kh8 61.Qf8+ Kh7 62.Rf7#; 59... Kh8 60.Rf8#) 60.Rf8 wins.

A.2) 57... Kh6 58.Rxf6 with an extra pawn (58... Rxa5 59.Qb1 and mate soon).

A.3) 57... Kh8 58.Qb8+ Ng8 59.Qe5+ and mate in two.

B) 56... Kg7 57.Rxf7+ Kh8 (57... Kg8 58.Qb8+ Ne8 59.Qxe8#) 58.Qb8+ (or 58.Rh7+ and mate in two) 58... Ng8 59.Rh7#.

C) 56... Kg8 57.Rb8+ Kg7 (57... Ne8 58.Rxe8+ Kg7 59.Qc3+ and mate in two) 58.Ne6+

C.1) 58... fxe6 59.Qb7+ Nd7 60.Qxd7+ Kf6 61.Rf8+ Ke5 (61... Kg5 62.Qe7#) 62.Qc7+ Ke4 63.Rf4+ Kd3 64.Rd4#.

C.2) 58... Kh7 59.Nf8+

C.2.a) 59... Kh8 60.Ne6+ Kh7 (60... Ng8 61.Qc3+ f6 62.Qxf6+ Kh7 63.Qg7#) 61.Nf8+ repeats moves.

C.2.b) 59... Kg8 60.Ne6+ Kh7 (60... Ne8 61.Rxe8+ doesn't improve Black's chances) 61.Nf8+ as above.

C.2.c) 59... Kg7 60.Ne6+ repeats moves.

D) 56... Kh8 57.Rb8+ Kg7 (57... Ng8 58.Qc3+ and mate in two) 58.Ne6+ transposes to C.

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The alternative 56.Rxf7+ Kg8 57.Qb8+ (57.Qxa2 Qxa2 58.Rxf6 Qxa5 59.Rxg6+ Kh7 and the a-pawn decides the game) 57... Kxf7 58.Qxa7+ Ke8 (58... Ke6 59.Nd4+ and 60.Nxe2 + -) 59.Qb8+ Ke8 doesn't seem to achieve more than a risky perpetual.

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The only remaining move is 56.Nd2 Q(R)xd2 (56... Kg7 57.Qxa2 wins) 57.Rxf7+ Kg8 (57... Kh8 58.Qb8+ Ng8 59.Qe5+ Nf6+ 60.Qxf6+ Kg8 61.Qg7#) 58.Rxf6 is similar to A above.

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I wasted too much energy trying to make 56.Ng5+ work, the move which at first glance looked more promising to me.

If I remember correctly it was Timman who said that 50% of lines are unimportant but we don't know which half in advance...

I wasted a lot of time on 56.Rxf7+ before realizing it doesn't work. Then I moved on to 56.Ng5+ only to find a draw with best play.

White has something better. After 56 Nd2 Rxd2 57 Rxf7+ Kg8 white wins with 58 Rxf6.

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White now has a mate threat beginning with 59 Qb8+. If 58...Kg7 then 59 Rf3 (or Rf4).

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Black now cannot prevent 60 Qb8 seeing 61 Qf8+ without giving up his queen. If he tries 59...Rb2 then 60 Qc3+ is a forced mate.

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Stockfish 7 gives mate in 16

That was my reaction when I looked at the answer to today's Saturday puzzle and saw the strong clearance and obstruction move 56. Nd2!

My weaker attempt (computer's third choice) at getting out of trouble and avoiding a Black mate was 56. Qxa2 Qxa2 57. Rxf7+ Kh8 58. Rxf6 with a difficult and unclear position for both sides.

The game move and puzzle solution 56. Nd2! gets White out of trouble and as a bonus yields a strong winning position.

If Black captures the obstructing Knight with either the Queen or the Rook, White gets a winning attack with his heavy pieces against the more exposed Black King.

Following the Rook capture line with 57. Rxf7+ Kg8 58. Rxf6 (diagram below),

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Deep Fritz 15 at 23 depth calculates a mate in 79 moves after 58...Kg7 59. Rf4 .

Following the Queen capture line with 56... Qxd2 57. Rxf7+ Kg8 58. Rxf6 (diagram below)

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Deep Fritz 15 at 20 depth calculates a clear win for White after 58. Rb2 Qa3 (+4.99 @ 20 depth, Deep Fritz 15).

In the game Black saw the Knight was poison and opted instead for 56...Kg8 57. Qxa2 .

Black could have gone for a cheapo draw with 57...Nxg4!? when 58. hxg4? allows a draw by repetition after 58...Qxg4+ =.

However, after 57....Nxg4!? White preserves the win with 59. Kh1! (diagram below)

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as the threat of 59...Kxf7 60. fxe3 (+2.34 @ 19 depth, Deep Fritz 15) proves decisive.

According to the computers, White had a much stronger continuation after 56...Kg8 with the in-between move sequence 57. Rb8+ Kg7 58. Qxa2 (+9.48 @ 18 depth, Deep Fritz 15).

Thanks for posting that line.

<plumbst> <Ah, nice move by White - interfering the 2nd rank and opening up the f-file. 57.Rb8+ would've been a quicker win though.>

Yes, in the text black could have played 57...Nxg4, threatening 58...Qxf2+. This forces 58 Rxf7 and black has 58...Nxe3+, below, (protecting the d5 pawn first) and black can take the rook next move. (giving up his knight with white's next move.)

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But this scenario does not help after 57 Rb8+ as this forces 57...Kg7. Now after 58 Qxa2, below, black playing either 58...Nxg4 or 58...Ne4 loses to 59 Qb2+ and white keeps his rook advantage.

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Thank you!

<I wasted a lot of time on 56.Rxf7+ before realizing it doesn't work. Then I moved on to 56.Ng5+ only to find a draw with best play.>

When I started typing my post I thought 56.Ng5+ was the winning move with a won ending or a forced mate and the other two not so direct or even losing. However, I was unable to fix the C.2 lines.

<<Perhaps you know whether Dan Heisman has some advice about detecting the right half.> Kind of. He says to "look wide before you look deep". But sometimes I don't think it is unavoidable--it takes calculation to find the nuances and sometimes dismiss a candidate completely. Dan would identify the killer move, ...Qxf2+ and ask "What are all the candidates that immediately stop the threat?">

That's why I consider the opponent's threats immediately after counting the material and before elaborating a solution.

<Then he teaches to look at least 3-ply with each candidate and find out which candidates can be dismissed right away, if any. So in the case of 56.Nd2, at 4-ply ahead 56...Rxd2/Qxd2 57.Rxf7+ Kg8 58.Rxf6 leaves it at least a viable candidate at that point. It's not easy to dismiss any one of the candidates Rxf7+, Ng5+, or Nd2 in short order so you pretty much have to examine each. But I think you did the right thing by examining Ng5+ in detail. Dan may suggest "progressive deepening" where you look at each candidate progressively deeper, switching between them--at least that's my understanding.>

I think Kasparov used to follow a similar method. I remember he mentioned something about this in 'How Life Imitates Chess'.

<For me, that taxes my visualization skills too much--I'm better off continuing on the same candidate and then moving on to the next after I'm done!>

It obviously requires a lot of concentration, discipline and energy.

white has no move to protect f2, and preparing flight with Kg3 seems grim. Ng5+ pxg5 or Nd2 Rxd2 seem pointless.

56. Rxf7+ Kh8 puts the K on the back rank but Qb8+ loses the R, and Qb7 to hold the R allows black's attack.

the escape appears to be an evaporation strategy:

56. Qxa2 Qxa2
57. Ne5 Qxa5
58. Rxf7+ Kg8
59. Rxf6

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My (sub-perfect) thinking:

I saw the twin objectives of (1) attack black's king and (2) don't get mated by ..Qxf2+ etc. To do both, have to move the Nf3 with tempo so that I can follow with Rxf7+ and Rxf6 such that my rook guards Pf2.

So I opened with <56.Ng5+>, expecting <56...hxg5>

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Now I have <57.Rxf7+ Kg8 58.Rxf6 Kg7 59.Rf3>

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My rook is preventing ...Qxf2, and I threaten Qb7+ which carries a potent attack in store that black is ill-equipped to stop.

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Checking with the computer: The good news is that the final position in my line above is mate in 22! The bad news is that black had some better options.

First, instead of taking my N, black should play <56...Kg8!>, and with black threatening mate, all I can do is perpetual check: <57.Rb8+ Kg7 58.Ne6+>

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And now <58...Kh7!>, since 58...fxe6? 59.Qb7+ with mate to follow.

Second, even if black takes N, <56...hxg5 57.Rxf7+> black is "less bad" with <57...Kh6>, and may even be able to salvage a draw after <58.Rxf6 Ra1 59.Qxd5 Qf1+ 60.Kg3 Qg1+ 61.Qg2 Qxg2 62.Kxg2 Rxa5>

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