The Matous Study: Solution Time
A couple of days ago, I presented a very elegant endgame study by M. Matous for the readers' solving pleasure (and if you solved it, I'm sure you'll agree that it was a pleasure), and now it's time for the solution. As with the Marshall-Capablanca game, I hope the reader will give solving this their best shot before looking at the solution; for those ready to take a look, click, read, and enjoy:
Matous,M, 1982
White is up loads of material here, but it's clear that a body count doesn't tell the whole story. For starters, Black is threatening to promote with b2-b1(Q). Second, the value of White's material advantage is diminished in that White can't afford to give up the rook, even for all three of the pawns, as two knights cannot force mate against a lone king except in the most extraordinary of circumstances. So it looks like White has to do the impossible: prevent promotion without giving up the rook. In fact, that may just turn out to be impossible, but let's see what we can do here, one move at a time, without worrying about whether it's a win or what will be sacrificed. So, for starters, we can see that the only way to prevent b2-b1(Q) - check - is to force the king to b1, and that limits our options to 1.Rd1+ and 1.Nc5. As 1.Rd1+ Kb2 leaves Black with the threat of 2...a1(Q)+, the other move must be better:
1.Nc5 b2 2.Nb3+ Kb1
That maneuver has bought White a little time and left the Black king in a more vulnerable location, but now it's time for a new idea. Can we exploit the Black king's location?
Well, if the pd4 were absent, we'd have 3.Nd5 a1(Q) 4.Nc3#. The pawn is there, however, so we don't have that mate, but there's another mating pattern: 3.Nd5/Nc6 a1(Q) 4.Nb4, and Black can't do anything to stop the threat of 5.Rd1#! (Note that in this line the pd4 is a detriment - it prevents Black from playing 4...Qa7+ and subsequently from using stalemate tricks to draw.)
Now that we have an idea, we have to figure out which move is right (if either). If 3.Nc6, then 3...d3 and 3...a1Q/R/B all allow the winning 4.Nb4 and 5.Rd1#, but Black has 3...a1(N)! White should probably play 4.Nxd4 in that position, but then the White knights aren't very well coordinated, as they're protecting each other instead of covering complementary squares.
Thus the right move is
3.Nd5 a1N
and now, so we can clear c3 for the Nd5,
4.Nxd4
Now White threatens, among other things, 5.Nc3+ Kc1 6.Rd1#, and if Black plays 4...Nb3 here, then 5.Nc3+ Kc1 6.Nxb3 is mate. Black has only one other try, but it's also quite strong:
4...Kc1
Now if White could protect the rook with either the Nd5 or the king, everything would be fine, as 5...b1(Q) would be met by 6.Ne2#. Unfortunately, the rook can't be protected by those pieces, and moving the knight to a safe square along the second rank will prevent a subsequent Ne2 from mating, as the knight will interfere with the rook's control of the second rank.
This is an obvious place for the solver to give up and start from scratch, but here is the moment where the composer reveals his genius. We saw that the combination of knights on b3 and c3 are quite powerful, at least as long as there's a piece preventing the Black king from escaping to c2. That's the White rook's function here, but it doesn't really matter who does the job as long as it's getting done!
Therefore, White's next move ensures his knight's access to b3 while keeping the Black king bottled in:
5.Rc2+!!
Black must capture - 5...Kd1 6.Ne3+ and 7.Ne3#, or 5...Kc1 6.Nc3#
5...Nxc2 6.Nb3+ Kd1
- and now...we stop a moment. 7.Nc3+ isn't quite mate; worse, there's no way to follow up after 7...Ke1. So we need to use the king to lock him in - but do we play 7.Kf1 or 7.Kf2? What difference could it make?
Well, as with the similar dilemma on move 3, we need to figure out Black's defense. Let's suppose we play 7.Kf2, threatening 8.Nc3 mate. The only way Black can defend is by promoting to another knight, and then we have a very interesting position in which all four knights are in zugzwang: a White knight move releases the mating net, while a Black knight move allows either 9.Nc3# or 9.Ne3#. White must therefore move the king, and to a square that keeps e1 covered: 8.Kf1. Unfortunately, Black can then play 8...Nd2 - check - and then the mate has been thwarted.
Therefore, by process of elimination, we have
7.Kf1! b1N 8.Kf2
and it's mate next move. [8.Kf2 Nd2 9.Nc3# offers the most visually attractive pattern, though it's thematically less valuable as Black's failure to escape via d2 is overdetermined.]
1-0
(show)
Matous,M, 1982
White is up loads of material here, but it's clear that a body count doesn't tell the whole story. For starters, Black is threatening to promote with b2-b1(Q). Second, the value of White's material advantage is diminished in that White can't afford to give up the rook, even for all three of the pawns, as two knights cannot force mate against a lone king except in the most extraordinary of circumstances. So it looks like White has to do the impossible: prevent promotion without giving up the rook. In fact, that may just turn out to be impossible, but let's see what we can do here, one move at a time, without worrying about whether it's a win or what will be sacrificed. So, for starters, we can see that the only way to prevent b2-b1(Q) - check - is to force the king to b1, and that limits our options to 1.Rd1+ and 1.Nc5. As 1.Rd1+ Kb2 leaves Black with the threat of 2...a1(Q)+, the other move must be better:
1.Nc5 b2 2.Nb3+ Kb1
That maneuver has bought White a little time and left the Black king in a more vulnerable location, but now it's time for a new idea. Can we exploit the Black king's location?
Well, if the pd4 were absent, we'd have 3.Nd5 a1(Q) 4.Nc3#. The pawn is there, however, so we don't have that mate, but there's another mating pattern: 3.Nd5/Nc6 a1(Q) 4.Nb4, and Black can't do anything to stop the threat of 5.Rd1#! (Note that in this line the pd4 is a detriment - it prevents Black from playing 4...Qa7+ and subsequently from using stalemate tricks to draw.)
Now that we have an idea, we have to figure out which move is right (if either). If 3.Nc6, then 3...d3 and 3...a1Q/R/B all allow the winning 4.Nb4 and 5.Rd1#, but Black has 3...a1(N)! White should probably play 4.Nxd4 in that position, but then the White knights aren't very well coordinated, as they're protecting each other instead of covering complementary squares.
Thus the right move is
3.Nd5 a1N
and now, so we can clear c3 for the Nd5,
4.Nxd4
Now White threatens, among other things, 5.Nc3+ Kc1 6.Rd1#, and if Black plays 4...Nb3 here, then 5.Nc3+ Kc1 6.Nxb3 is mate. Black has only one other try, but it's also quite strong:
4...Kc1
Now if White could protect the rook with either the Nd5 or the king, everything would be fine, as 5...b1(Q) would be met by 6.Ne2#. Unfortunately, the rook can't be protected by those pieces, and moving the knight to a safe square along the second rank will prevent a subsequent Ne2 from mating, as the knight will interfere with the rook's control of the second rank.
This is an obvious place for the solver to give up and start from scratch, but here is the moment where the composer reveals his genius. We saw that the combination of knights on b3 and c3 are quite powerful, at least as long as there's a piece preventing the Black king from escaping to c2. That's the White rook's function here, but it doesn't really matter who does the job as long as it's getting done!
Therefore, White's next move ensures his knight's access to b3 while keeping the Black king bottled in:
5.Rc2+!!
Black must capture - 5...Kd1 6.Ne3+ and 7.Ne3#, or 5...Kc1 6.Nc3#
5...Nxc2 6.Nb3+ Kd1
- and now...we stop a moment. 7.Nc3+ isn't quite mate; worse, there's no way to follow up after 7...Ke1. So we need to use the king to lock him in - but do we play 7.Kf1 or 7.Kf2? What difference could it make?
Well, as with the similar dilemma on move 3, we need to figure out Black's defense. Let's suppose we play 7.Kf2, threatening 8.Nc3 mate. The only way Black can defend is by promoting to another knight, and then we have a very interesting position in which all four knights are in zugzwang: a White knight move releases the mating net, while a Black knight move allows either 9.Nc3# or 9.Ne3#. White must therefore move the king, and to a square that keeps e1 covered: 8.Kf1. Unfortunately, Black can then play 8...Nd2 - check - and then the mate has been thwarted.
Therefore, by process of elimination, we have
7.Kf1! b1N 8.Kf2
and it's mate next move. [8.Kf2 Nd2 9.Nc3# offers the most visually attractive pattern, though it's thematically less valuable as Black's failure to escape via d2 is overdetermined.]
1-0
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