John Nunn's Favorite Puzzles Tutorial



1.
[{B:rnbqkbnr/pppppppp/32/PPPPPPPP/RNBQKBNR}
These puzzles are a collection of 50 of the favorites of British Grandmaster John Nunn.  Not only are they a fun way to take a break from the tough competition and lengthy time of a whole game, they are also an outstanding way to practice and learn. Puzzles like these are available in most newspapers and chess publications, so if you find yourself hooked after solving these, you have plenty of resources.]

2.
[{B:2kr4/K1pp4/8/8/8/8/7Q/3R4}
{V:This problem was composed by Max Euwe, who was World Champion from 1935 to 1937, and it provides a nice introduction to the 50 puzzles. White to play and mate in two. Try your solution on the board.;h2d6;Correct, White prevents the defense ...d6 in the most dramatic way possible, by offering a queen sacrifice. Although there is no threat, every Black move creates a weakness which allows mate. After 1...c6 (or c5) White can play 2 Qb8 mate, while if the rook moves then d7 is not guarded, so White can play 2 Qxd7 mate. Finally, if Black accepts the sacrifice by 1...cxd6, then 2 Rc1 is mate.;Incorrect.;It is worth looking to see if Black has a strong defense already arranged. If so, then White's first move must either prevent it or prepare a reply. Here Black has the possibility to play ...d6, making it hard to see how White is going to deliver mate. So White must try to prevent ...d6.}]

3.
[{B:b7/N3B3/Q7/3kpp2/3p4/1R4P/9/7K}
{V:White's pieces are clustered menacingly around Black's king, but it is far from easy to force mate in two. White to play and mate in two.;a6a2;Correct;Incorrect.;The first point to note is that Black's king has a possible escape route to e4, so White's first move must either prevent ...Ke4 or prepare a reply to it. The second point is that if White loses control of c4 or e6, then Black can give a discovered check by moving his king. However, composers love an element of paradox in their problems, so ...}]

4.
[{B:b7/N3B3/Q7/3kpp2/3p4/1R4P/9/7K}
The arrangement of bishop on a8 and white king on h1 appears to make life hard for White, because it creates the possibility of a discovered check by Black if, for example, the queen moves and allows either ...Kc4+ or ...Ke6+. But this is precisely the sort of deception composers like to incorporate into their problems; the idea is that the solver will see the discovered checks and therefore reject a queen move....But it turns out that the key is with the queen after all. Black is allowed his bit of fun, but the queen is ambushed behind the rook, and White can trump Black by meeting his discovered checks with discovered mates! The threat is 2 Re3 mate, and the queen move prepares to meet 1...Ke4 by 2 Qg2 mate. Black can stop the threat by 1...d3, but then 2 Rb4 is mate, while 1...e4 is answered by 2 Rb5 mate. The two star variations arise from the other moves of Black's king, 1...Kc4+ allows 2 Rf3 mate (the rook must guard d3), and 1...Ke6+ allows 2 Rb7 mate (the rook must guard d7 and e7). Altogether, White's rook delivers a total of five different mates.]

5.
[{B:3brrb1/2N4B/8/2p4Q/2p2k2/5P2/4P1KR/2N2RB}
{V:At the moment all White's mating threats are covered by the four black pieces on the back rank, so how can White break the deadlock? White to play and mate in two.;h2h1;Correct;Incorrect.;If you check Black's available moves, you will find that all but two of them allow mate in one. So you need to find the two defenses, and work out how White can set up a mating reply for them.}]

6.
[{B:3brrb1/2N4B/8/2p4Q/2p2k2/5P2/4P1KR/2N2RB}
White cannot mate immediately because of the pieces on the back rank, for example Rh4 mate is prevented by the bishop on d8. Likewise, the other pieces stop e3 mate, Qf5 mate and Nd5 mate. But the fact that each Black piece has a responsibility proves to be Black's undoing, because they can hardly move without stepping on each other's toes. After 1...Re7, for example, White can play 2 Rh4 mate, while 1...Re6 blocks the other bishop and allows 2 Nd5 mate. Indeed, in the diagram position Black has only two moves which cannot be met by immediate mate, namely 1...Bg5 and 1...Re3. If only White can find a way to prepare mates for these moves, then Black will be obliged to fatally weaken himself. What weakness is created by 1...Re3? The answer can only be that it blocks e3, and therefore the bishop on g1 is freed to deliver mate by Bh2. Thus the first move must be with the rook on h2, but should it move to h1 or h3? The answer is provided by the other possible defense, 1...Bg5. This blocks g5 and frees the queen to mate by Qh2. So the solution is the unlikely-looking 1 Rh1! There is no threat, but nevertheless Black has no defense. Here is the full list of variations.
1...Re7/Rf6/Bxc7/Bh4 2 Rh4 (or Rxh4)
1...Re6/Rf7/Bxh7/Bd5 2 Nd5 (or Nxd5)
1...Re5 2 Qg4
1...Re4 2 fxe4
1...Re3 2 Bh2
1...Rxe2+ 2 Nxe2
1...Be7/Be6 2 e3
1...Bf6/Bf7/Rf5 2 Qf5 (or Qxf5)
1...Bg5 2 Qh2
1...c3 2 Nd3]

7.
[{B:1b6/1B2pQ2/8/4k1B/3r4/1N1R4/5n2/1K5b}
{V:White to play and mate in 2. Try your solution on the board.;b7e4;Correct;Incorrect.;
Black has a whole range of powerful threats, including 1...Nxd3 and 1...Bxb7, so White's first move has to be fairly blunt. A sacrifice may be necessary.}]

8.
[{B:1b6/1B2pQ2/8/4k1B/3r4/1N1R4/5n2/1K5b}
Since Black threatens to play 1...Nxd3 or 1...Bxb7, White's first move must carry a strong threat. Bearing in mind that sacrifices are appealing to both composer and solver alike, one might be led to try 1  Be4! This multiple bishop sacrifice is the spectacular solution. The powerful threat is 2 Qxe7 mate. If Black plays 1...Kxe4, then 2 Re3 is mate; 1...Rxe4 allows either 2 Rd5 or 2 Qd5 mate, while if Black plays 1...Nxe4 or 1...Bxe4 then the square e4 is blocked and White can mate by 2 Bf4. Thus the sacrifice can't be accepted, but other moves are no help, for example 1...Bd6/Rd6/Rd7 2 Qf5 mate, or 1...e6 2 Qf4 mate.]

9.
[{B:8/2K1Qp1b/2p5/1k6/8/RBp3r/9/1R6}
{V:White to play and mate in two. Try your solution on the board.;c7d6;Correct;
Incorrect.;Black threatens to take on b1, so White must create a strong threat. At the moment his queen is under-employed, doing nothing more than cover b4 and c5, a job which could equally well be performed by a bishop. How can White make use of the lateral powers of his queen?}]

10.
[{B:8/2K1Qp1b/2p5/1k6/8/RBp3r/9/1R6}{S:c7d6}
Sometimes the solution to a problem cannot be deduced by a purely sequential reasoning process - a leap of the imagination is required. It seems likely that White's queen will be involved, because at the moment she is not using her full powers, but how exactly?  1  Kd6! This certainly brings the queen into the game, because it creates the threat of 2 Qb7 mate, but otherwise it appears to be one of the most unlikely moves on the board. Not only does it allow Black's king to flee to b4, it also permits Black's rook to deliver check on either d3 or g6. However, both these checks block the h7-bishop's attack on b1, allowing White to give mate by discovery  1...Rd3+ 2 Bd5 mate or 1...Rg6+ 2 Be6 mate. The only other move to meet the threat is 1...Kb4, but this leads to the third mate by discovery after 2 Kxc6.]

11.
[{B:8/8/8/2N5/B1p1Q3/4n3/p3R3/B1kn2K}
{V:White to play and mate in two. Try your solution on the board.;e4b7;Correct;
That is incorrect.;A close look at Black's possible moves shows that in every single case White can reply with an immediate mate. It follows that a waiting move would solve the problem. But this is another typical example of deception by the composer. The solver is tempted to look for a way of preserving the status quo, but the solution depends on abandoning preconceived ideas and finding alternative ways of coping with Black's defenses.}]

12.
[{B:8/8/8/2N5/B1p1Q3/4n3/p3R3/B1kn2K}
All Black's moves allow immediate mate, for example if the d1-knight moves, then Bb2, or if the e3-knight moves then Qc2. Finally, 1...c3 allows 2 Nb3 mate. A waiting move would solve the problem, but there are no waiting moves, for example 1 Kh1? Nf2+, 1 Kh2? Nf1+, 1 Rg2? Nf2 or 1 Qg6? Nf5. The composer has arranged it so that the solver's natural inclination to preserve the existing mates leads to a dead end, and only some lateral thinking can provide the answer. White must retain control of b1, or else ...Kb1 prevents a mate, so it isn't too hard to find this move, even though it gives up all the mates already prepared. Now Black's moves are answered by a completely new set of mates, if the d1-knight moves, then 2 Qb2 (instead of 2 Bb2), if the e3-knight moves, then 2 Rc2 (instead of 2 Qc2) and finally if 1...c3, then 2 Nd3 (instead of Nb3).]

13.
[{B:7k/1R5P/8/8/5P2/3B1Q2/8/2K5}
{V:White to play and mate in three.  Try your solution on the board.;b7b1;Correct;
Incorrect.;The first move must be with the rook, in order to lift the stalemate. The key is to find the right square, but this is not obvious until you have found White's second move. So try a random move, such as 1 Rb3, forcing Black to reply 1...Kg7. Now how should White continue? After White moves the rook and Black replies 1...Kg7, White should play 2 Qb7+. Black's main replies are 2...Kf6 and 2...Kh8. Which is the only square for the rook which allows White to cope with both these replies?}]

14.
[{B:7k/1R5P/8/8/5P2/3B1Q2/8/2K5}
{D:100}{S:b7b8}
Try 1 Rb8+?
Problems in less than six moves very rarely begin with a check, which should be a warning signal that this is not correct.  1...Kg7  2  h8=Q+   Kf7  and there is no mate.]

15.
[{B:7k/1R5P/8/8/5P2/3B1Q2/8/2K5}
{D:100}{S:b7g7}
Try 1  Rg7.
Almost everybody tries this move, but it cannot be better than a 'nothing' rook move such as Rb3, and as problems have only one solution, 1 Rg7 cannot be correct.  1 ...Kxg7 and there is no mate in three.]

16.
[{B:7k/1R5P/8/8/5P2/3B1Q2/8/2K5}
{D:100}{S:b7b1}
1  Rb1!
Why here and nowhere else? The reason only becomes apparent after 1... Kg7  2  Qb7+.  This is the right way to close the net around Black's king.  Now 2...Kf8 and 2...Kh6 are met by 3 h8Q mate and 2...Kf6 by 3 Rb6 mate (this explains why 1 Rb8+ didn't work; the queen would block the rook and prevent it returning to b6). Finally  2...Kh8 3  Qb2  mate. And now we can see why, paradoxically, the rook had to go all the way back to b1.]

17.
[{B:2R5/kpb1P1P/1p6/1P6/K7/8/8/8}
{V:White to play and mate in three. Try your solution on the board.;c8h8;
Correct;Incorrect.;The obvious move is 1 e8Q (or 1 g8Q), but Black replies 1...Bb8 and if White takes the bishop then Black is stalemated, while otherwise Black continues with 2...Ka8 and there is no mate. But now comes a typical piece of lateral thinking - if only White's queen and rook were the other way round on the eighth rank, then ...Bb8 wouldn't be a defense. How can White achieve this?}]

18.
[{B:2R5/kpb1P1P/1p6/1P6/K7/8/8/8}
If White promotes a pawn immediately by 1 e8Q or 1 g8Q, then Black replies 1...Bb8, and White cannot take the bishop because of stalemate, so there is no mate in two. The correct plan is to arrange for the rook to be on the other side of the queen, so that ...Bb8 is no longer an effective defense. However, 1 Rg8? (1 Rf8? is also met by 1...Bd6) fails to 1...Bd6 2 e8Q Bf8, blocking the back rank.]

19.
[{B:2R5/kpb1P1P/1p6/1P6/K7/8/8/8}
{S:c8h8}
The rook must go to the very end, so as to give White a choice of promotions. White doesn't threaten anything, because 2 e8Q and 2 g8Q would be met by ...Bd8, but Black's bishop cannot stay on c7. After 1...Bd6 White plays 2 g8Q, intending Qa8 mate, while if the bishop moves to any other square on the b8-h2 diagonal, White forces mate by 2 e8Q.]

20.
[{B:7R/kpb1P1P1/1p6/1P6/K7/8/8/8}
{S:c7d8}
1...Bd8.  The best defense.
2 e8Q? and 2 g8Q? are met by 2...Kb8, while 2 exd8Q? is stalemate.]

21.
[{B:3b3R/kp2P1P1/1p6/1P6/K7/8/8/8}
{S:e7d8}{P:WBd8}
2  exd8B!   White avoids stalemate by underpromoting. Once again there is no threat, but Black's king is forced to move onto the dangerous back rank.   2...Kb8  3  Bxb6 mate.]

22.
[{B:8/pk1B4/p7/2K1p3/8/8/4Q3/8}
{V:White to play and mate in three. Try your solution on the board.;d7h3;Correct;
Incorrect.;Black threatens to play ...Kc7, when White's bishop will be attacked. If White spends a tempo saving the bishop, then he will have little chance of mating in three. So suppose White plays 1 Bf5, for example. Black replies 1...Kc7, and after 2 Qxa6, threatening mate on c8, the king just runs away by 2...Kd8. How can White improve on this line by again aiming to mate on c8, but at the same time preventing 1...Kc7 followed by 2...Kd8?}]

23.
[{B:8/pk1B4/p7/2K1p3/8/8/4Q3/8}
White's main problem is to deal with Black's defense 1...Kc7. The temptation is to prevent ...Kc7 directly by playing 1 Qxe5, but then Black replies 1...a5 and, even though White's pieces appear very menacing, there is no mate in two. 1 Qh5 is a cunning idea, so that 1...Kc7 can be met by 2 Qe8 and 3 Qc8 mate, but again 1...a5 is a satisfactory defense. This leads to the idea of transferring the queen to c8 by another route, but after 1 Bf5 Kc7 2 Qxa6, for example, Black slips away by 2...Kd8.]

24.
[{B:8/pk1B4/p7/2K1p3/8/8/4Q3/8}
{S:d7h3}
This surprising move clears the way for 2 Qg4 and 3 Qc8 mate. It also copes with the defense 1...Kc7 2 Qg4 Kd8, because White has the mate 3 Qd7 ready. Black has only one way to meet the threat.  1...a5  If now 2 Qg4, then 2...a6 and Black has created a flight square for his king on a7. While the move 1...a5 has prevented one mate, it has opened the door to another, far more spectacular, possibility.  2  Qa6+!  White suddenly changes plans and sacrifices his queen.  2...Kxa6  Forced, or else Qc8 mates.  3  Bc8 mate.]

25.
[{B:1q5k/4R3/8/8/1p6/1B6/5R2/1K6}
{V:White to play and mate in three. Try your solution on the board.;f2a2;
Correct;Incorrect.;The e7-rook and b3-bishop box Black's king into the corner, so if only White could check with his other rook, it would be mate. But the obvious moves by the f2-rook don't work, because Black's queen is able to cover both the potential mating squares, for example after 1 Rf6? Qf4! or 1 Rg2? Qg3! Black can exploit a stalemate defense. So how about trying a non-obvious move?}]

26.
[{B:1q5k/4R3/8/8/1p6/1B6/5R2/1K6}
{S:f2a2}
White only needs to give a check with his f2-rook and Black will be mated. But how is the rook to avoid the unwelcome attentions of Black's queen? All the obvious moves allow the queen to cover both mating squares, the one on the h-file and the one on the eighth rank. After 1 Rf1? Qa8, 1 Rf7? Qg8 or 1 Rf3? Qc8 White hasn't achieved anything, 1 Rf5? Qe8! may win the queen but it doesn't mate in three, while in the lines 1 Rg2? Qg3! and 1 Rc2? Qc7! Black uses a stalemate defense to stay White's hand. If White plays Bc4, Black replies with 1...Qb3. Perhaps the most unlikely-looking square for the rook, but there is a kind of logic behind it. The other rook moves failed because Black's queen could always move so as to cover the two potential mating squares. Playing the rook to a2 succeeds because Black's queen is already covering the mating squares at a8 and h2. If Black could pass he would be safe, but he has to move his queen, which is obliged to abandon control of either a8 or h2, for example 1...Qg3 2 Ra8+ or 1...Qg8 2 Rh2+.]

27.
[{B:4r1b1/1p4B1/pN2pR2/RB2k3/1P2N2p/2p3b1/n2P1p1r/5K1n}
{V:This is one of the most famous problems ever composed, and I apologize to those who have seen it before, but I am sure they will appreciate the pleasure it will give to those who do not know the solution. White to play.;f1e2;Surprisingly, the many discovered checks available from rook and bishop don't lead anywhere, since the black king can escape by moving to d4 or e4. Solving this problem requires a massive suspension of disbelief.;Incorrect.;A typical solver, 'I've tried just about every legal move, and nothing seems to work. All those checks with the rook and the bishop don't seem to lead anywhere ... well, since I've tried all the sensible moves, I might as well look at the ridiculous ones. What about 1 ***? No, that's just too stupid - Black can simply reply 1...*** and I'll just have to go back again. Hang on a moment, maybe I don't have to go back  ... no, that can't possibly work, it's absurd ... but I don't see exactly why it doesn't work. Perhaps it does work ... yes, unbelievable!' Now all you have to do is fill in the blanks.}]

28.
[{B:4r1b1/1p4B1/pN2pR2/RB2k3/1P2N2p/2p3b1/n2P1p1r/5K1n}
{S:f1e2}
This is the stunning key. White not only allows Black to promote his pawn, but to give double check at the same time. The threat is 2 Rf7+ (or, indeed, anywhere else on the f-file) Kxe4 3 Bd3 mate. If Black doesn't promote his pawn, then the influence of the active white king proves the straw that breaks the camel's back, for example 1...Nxb4 2 Bd3+ Kd4 3 dxc3 mate, 1...Kxe4 2 Bd3+ Kd4 3 Rf4 mate, 1...Kd4 2 Rf4+ e5 3 Nxg3 mate, 1...Nc1+ 2 Ke3 Bf4+ 3 Rxf4 mate or 1...Rd8 2 Ke3 followed by mate from rook or bishop.]

29.
[
{S:f2f1}{P:BQf1}
1...f1Q+
Who could resist this move? At first sight White has to play 2 Kxf1, but then any chance of a mate in three has gone right out of the window.]

30.
[
{S:e2e3}
2 Ke3!!
From surprising to totally unbelievable. White just ignores the new queen, and leaves Black's pieces to do their worst. Someone glancing quickly at the position might think that Black should be able to mate in one, but in fact Black can't avoid a mate in one himself! Despite having ten different checks available, in every case White can mate by discovery with either the b5-bishop or the f6-rook.]

31.
[{B:7k/8/5N1P/8/2p5/2N5/8/3K3R}
{V:This is a gentle introduction to the longer problems. White only needs to give check in order to mate, but at the same time he must avoid stalemating black. White to play and mate in four.;c3b1;Correct;Incorrect.;All the obvious moves either lead to stalemate, or allow Black to promote with check and thereby delay the mate beyond the fourth move. One example is 1 Nb5 c3 2 Ke2 c2 3 Rg1 c1N+ and White has to waste a tempo moving his king again. But if White could force Black to promote his pawn on a different square, he would no longer be able to promote with check and White would save a tempo. How can this be achieved?}]

32.
[{B:7k/8/5N1P/8/2p5/2N5/8/3K3R}
{S:c3b1}
The answer is Nb1. After 1 Ncd5, for example, Black plays 1...c3 2 Rg1 c2+ and White has the choice between stalemating Black and allowing a promotion with check (for example, 3 Ke2 c1N+) when mate in four is impossible. The same problem arises after all the other moves of the c3-knight, except for one. White's plan is to force Black to promote on b1 instead of c1, when he will not be in a position to check White's king.]

33.
[{B:7k/8/5N1P/8/2p5/8/8/1N1K3R}
{S:c4c3}
1...c3.]

34.
[{B:7k/8/5N1P/16/2p5/8/1N1K3R}
{S:d1e2}
2 Ke2]

35.
[{B:7k/8/5N1P/16/2p5/4K3/1N5R}
{S:c3c2}
2...c2]

36.
[{B:7k/8/5N1P/24/2p1K3/1N5R}
{S:h1c1}
3  Rc1!
The only way to prevent a promotion on c1 is to block the square with the rook. Thanks to White's first move, Black is not stalemated.]

37.
[{B:7k/8/5N1P/24/2p1K3/1NR5}
{S:c2b1}{P:BQb1}
3...cxb1Q.]

38.
[{B:7k/8/5N1P/24/4K3/1qR5}
{S:c1c8}
4  Rc8 mate.]

39.
[{B:8/1Q1K3n/1B6/1k6/8/8/1P6/8}
{V:White to play and mate in four. Try your solution on the board.;b7a6;Correct;
Incorrect.;Black's main defense is to run away with his king by ...Kc4. This must be prevented, even at the cost of extreme measures.}]

40.
[{B:8/1Q1K3n/1B6/1k6/8/8/1P6/8}
{S:d7d6}
Try 1 Kd6? Nf6 (but not 1...Ng5? 2 Ba5+ Kxa5 3 Kc6 and mates by Qb5) 2 Ba5+ Kc4 and now there is no mate on d5.]

41.
[{B:8/1Q1K3n/1B6/1k6/8/8/1P6/8} 
{D:100}{S:b6d4}
Try 1 Bd4+? Kc4 and the king slips away.]

42.
[{B:8/1Q1K3n/1B6/1k6/8/8/1P6/8}
{D:100}{S:b7c6}
Try 1 Qc6+? Kb4 and there is no mate.]

43.
[{B:8/1Q1K3n/1B6/1k6/8/8/1P6/8}
It is tempting to give a check with the bishop, but this would certainly be an unusually brutal start to a problem. In fact the bishop checks don't lead to mate, as Black replies ...Kc4. Most quiet moves fail because Black starts checking with his knight, delaying the mate beyond move four. If White avoids the knight checks by 1 Kd6, Black replies 1...Nf6! 2 Ba5+ Kc4 (not 2...Kxa5 3 Kc6) and the knight stops mate on d5, so the king escapes. This is a 'lateral thinking' type of problem, the solution can only be found by overcoming one's normal chess inhibitions.]

44.
[{B:8/1Q1K3n/1B6/1k6/8/8/1P6/8}
{S:b7a6}
1 Qa6+!
Problems less than six moves long rarely start with a check, so when a composer does incorporate a checking first move, it can be quite hard to find. Moreover, in such a simplified position there is a natural reluctance to part with White's most powerful piece.]

45.
[{B:8/3K3n/QB6/1k6/8/8/1P6/8}
{S:b5a6}
1...Kxa6
After  1...Kb4 2 Qd3 Black cannot prevent 3 Kc6 followed by 4 Qb5 mate.]

46.
[{B:8/3K3n/kB6/8/8/8/1P6/8}
{S:d7c6}
2  Kc6!
Now White's king is out of the black knight's range and there is no way to prevent 3 b4 and 4 b5 mate.]

47.
[{B:8/1p3K1p/8/5p2/2Q2P2/k1P4B/3R4/1q6}
{V:White to play and mate in four. Try your solution on the board.;h3f5;Correct;
Incorrect.;White would like to play Ra2+ followed by Qb4 mate, but the immediate 1 Ra2+ fails because 1...Qxa2 pins White's queen. On the other hand, White has no time for the cautious 1 Kf8, because then Black can bail out with 1...Qb2!, which delays mate beyond the fourth move. White must remove his king from the a2-g8 diagonal 
with gain of tempo. How?}]

48.
[{B:8/1p3K1p/8/5p2/2Q2P2/k1P4B/3R4/1q6}
The combination which leaps to the over-the-board player's eye is 1 Ra2+ Qxa2 2 Qb4 mate, but this doesn't work because ...Qxa2 pins White's queen. If White plays the preparatory 1 Kf8 (1 Kg7 is met the same way), then 1...Qb2! prevents Ra2+ and delays mate beyond the fourth move. Another idea is 1 Bg2, intending 2 Bd5 and then 3 Ra2+, but Black plays 1...b5 and White has to waste time moving the queen. White must move his king off the dangerous a2-g8 diagonal with gain of tempo, and this is where the bishop on h3 comes into the scene.]

49.
[{B:8/1p3K1p/8/5p2/2Q2P2/k1P4B/3R4/1q6}
{S:h3f5}
1 Bxf5!
The solution to White's dilemma, if Black doesn't take on f5, then the bishop has entered play with gain of tempo. Then White's attacking force is too much, for example 1...b5 2 Qc5+ Ka4 3 Bxb1, 1...Qb3 2 Be6! Qxc4 3 Bxc4 and 4 Ra2 mate, or 1...Qb2 2 Qc5+ Ka2 (2...Ka4 3 Rxb2 and 2...Kb3 3 Qb4+ also lead to mate) 3 Qa5+ Kb3 4 Be6 mate. And if Black does take on f5 ...]

50.
[{B:8/1p3K1p/8/5B2/2Q2P2/k1P5/3R4/1q6}
{S:b1f5}
1...Qxf5+]

51.
[{B:8/1p3K1p/8/5q2/2Q2P2/k1P5/3R4/8}
{S:f7e7}
2 Ke7!
Despite the open position, this careful choice of square leaves Black without a reasonable check. Black can give up his queen, but this only delays mate by one move. Consequently, there is nothing better than to stop the threatened mate on a2.]

52.
[{B:8/1p2K2p/8/5q2/2Q2P2/k1P5/3R4/8}
{S:f5b1}
2...Qb1
And now the original idea appears in full force.]

53.
[{B:8/1p2K2p/8/8/2Q2P2/k1P5/3R4/1q6}
{S:d2a2}
3 Ra2+]

54.
[{B:8/1p2K2p/8/8/2Q2P2/k1P5/R7/1q6}
{S:b1a2}
3...Qxa2]

55.
[{B:8/1p2K2p/8/8/2Q2P2/k1P5/q7/8}
{S:c4b4}
4 Qb4 mate.]

56.
[{B:k1K5/p7/P1N5/1P6/4pP2/2p1P3/pp6/r3Q3}
{V:White to play and mate in four. Try it on the board.;c6b4;Correct;
Incorrect.;White's main plan is to transfer his knight to c7. After 1 Nd8, for example, he threatens 2 Ne6 and 3 Nc7. At this stage it isn't obvious why 1 Nb4 and 1 Ne7 might be different, but of course it will turn out that only one of these three moves works. Black defends by 1...***, but White has the surprising reply 2 ***!, which appears to give White the time he needs to complete his knight maneuver. But then Black produces the truly imaginative defense 2...***!, which forces White to abandon his plan of playing the knight to c7. Now it suddenly becomes clear why White's first move is unique, because he needs to have the option of 3 *** with mate next move. Now just fill in the blanks.}]

57.
[{B:k1K5/p7/P1N5/1P6/4pP2/2p1P3/pp6/r3Q3}
Solving this problem is like peeling the layers off an onion. Attempting to bring the queen into the attack doesn't mate in four, for example 1 Qg3? Rg1! or 1 Qh4? Rh1! 2 Qd8 Rh7!, so White's main idea is to play his knight to c7. There are three possible routes, 1 Nd8, intending Ne6-c7, 1 Ne7, intending Nd5-c7 and 1 Nb4, intending Nd5-c7. At this stage it isn't clear why these three moves aren't equally good. This is the first layer.]

58.
[{B:k1K5/p7/P1N5/1P6/4pP2/2p1P3/pp6/r3Q3}
{S:c6b4}
1 Nb4!
Later on we will see why only this move works. Whichever knight move White chooses, Black has only one possible defense.]

59.
[{B:k1K5/p7/P7/1P6/1N2pP2/2p1P3/pp6/r3Q3}
{S:c3c2}
1...c2
If Black promotes with the check, then White's mating plans will be completely disrupted, so White must do something extraordinary to prevent 2...c1Q+.]

60.
[{B:k1K5/p7/P7/1P6/1N2pP2/4P3/ppp5/r3Q3}
{S:e1c1}
2 Qc1!
This spectacular move is the second layer. White simply blocks the c-pawn, preventing the check. Now it seems that Black's resources are at an end because neither 2...bxc1Q nor 2...b1Q stops White's knight tour to c7.]

61.
[{B:k1K5/p7/P7/1P6/1N2pP2/4P3/ppp5/r1Q5}
{S:b2b1}{P:BBb1}
2...b1B!
The third layer. This imaginative defense incarcerates Black's rook and sets up a stalemate. If White had chosen one of the other first moves, his knight would now be on either d8 or e7. In neither case would it be possible to mate in two, but with the knight on b4 there is one final layer ...]

62.
[{B:k1K5/p7/P7/1P6/1N2pP2/4P3/p1p5/rbQ5}
{S:b4d3}
3 Nd3!]

63.
[{B:k1K5/p7/P7/1P6/4pP2/3NP3/p1p5/rbQ5}
{S:e4d3}
3...exd3]

64.
[{B:k1K5/p7/P7/1P6/5P2/3pP3/p1p5/rbQ5}
{S:c1h1}
4  Qh1 mate.]

65.
[{B:q7/n2BNp2/5k1P/1p5P/1p2RP2/1K6/8/8}
{V:White to play and mate in six. Try your solution on the board.;e4e3;Correct;
Incorrect.;Black's queen has the responsibility of covering the potential mates by Ng8 and Nd5. This means that if it were Black to move, then he would have to allow mate in one, because any queen move loses control of one of the two critical squares, while a knight move necessarily obstructs the queen. However, White cannot maintain the status quo, and in fact he has few reasonable moves himself, since he cannot allow Black to start checking. This means that it should be possible to find the solution by a process of elimination.}]

66.
[{B:q7/n2BNp2/5k1P/1p5P/1p2RP2/1K6/8/8}
This is a curious position in which both sides are in a straitjacket. There are potential mates by Nd5 and Ng8, so Black's queen must maintain control of d5 and g8. This means that Black to move would have to allow immediate mate, since the queen cannot retain control of both squares, while a knight move would block the queen. It follows that a waiting move would force immediate mate, but White has no waiting moves available, for example 1 Kb2? b3, with ...b4 and ...Nb5 to come, or 1 Bg4? (or Bh3?) Qd8! (White's bishop move opened up the line d8-d5) threatening ...Qxe7.]

67.
[{B:q7/n2BNp2/5k1P/1p5P/1p2RP2/1K6/8/8}
{S:e4e3}
1 Re3!
Just about the only reasonable move. We have seen that the bishop and king cannot move, and White cannot allow ...Qf3+, so Re3 it is.]

68.
[{B:q7/n2BNp2/5k1P/1p5P/1p3P2/1K2R3/8/8}
{S:a8g2}
1...Qg2
This is why Re3 isn't an effective waiting move, Black's queen is given an alternative square from which to guard d5 and g8. Now Black threatens to disrupt the mating net completely by playing ...Nc6, so White must act quickly.]

69.
[{B:8/n2BNp2/5k1P/1p5P/1p3P2/1K2R3/6q1/8}
{S:d7g4}
2 Bg4
Cutting Black off from g8. Now 2...Qxg4 fails to 3 Nd5+ Kf5 4 Re5 mate, so Black's queen must rush back to the corner.]

70.
[{B:8/n3Np2/5k1P/1p5P/1p3PB1/1K2R3/6q1/8}
{S:g2a8}
2...Qa8
The situation differs from that at move one because White's bishop covers f3, so his rook is free to move off the third rank without allowing ...Qf3+.]

71.
[{B:q7/n3Np2/5k1P/1p5P/1p3PB1/1K2R3/8/8}
{S:e3e5}
3 Re5!
Black is again seriously short of moves. 3...Qf3+ allows 4 Bxf3 followed by a knight mate, and the knight cannot move, so the queen must continue her journeys.]

72.
[{B:q7/n3Np2/5k1P/1p2R2P/1p3PB1/1K6/8/8}
{S:a8d8}
3...Qd8
Threatening ...Qxe7, or a check on the d-file, but White has a reply which not only meets these threats, but also gently tightens the net around Black's king.]

73.
[{B:3q4/n3Np2/5k1P/1p2R2P/1p3PB1/1K6/8/8}
{S:g4d7}
4 Bd7
Black cannot play 4...Qxe7 because of 5 Rf5 mate, so again the queen has no choice.]

74.
[{B:3q4/n2BNp2/5k1P/1p2R2P/1p3P2/1K6/8/8}
{S:d8a8}
4...Qa8
But now White reveals the point behind all his maneuvers ...]

75.
[{B:q7/n2BNp2/5k1P/1p2R2P/1p3P2/1K6/8/8}
{S:e5e4}
5 Re4
This returns to the initial position, but with Black to move instead of White. As we mentioned at the start, this means that White can mate next move. The white rook was the hero of the solution, since the round trip Re4-e3-e5-e3 was the key loss of tempo, but the bishop's outing to g4 and back again was the catalyst that made the whole thing work. Black's poor queen deserves some sympathy; she ran back and forth trying to hold Black's position together, but all to no avail.]

76.
[{B:n1N3br/2p1Bpkr/1pP2R1b/pP1p1PpR/Pp4P1/1P6/1K1P4/8}
{V:The position is certainly congested, but most of the pieces don't move during the solution, so this problem is easier than it might appear. White to play and mate in six.;h5h1;Correct;Incorrect.;Black can only move his d-pawn, so after ...d4 and ...d3 he will be stalemated. This gives White two free tempi to do with as he pleases, before he has to worry about lifting the stalemate. If the pawn on a5 were missing, then White would be able to wait until Black played 2...d3, and then mate by 3 Bxb4 Kxf6 4 Bc3. At the moment the chain of black pawns on the queenside stops this idea by denying the bishop any squares on the e7-a3 diagonal. How can White use his spare tempi to unblock the queenside logjam?}]

77.
[{B:n1N3br/2p1Bpkr/1pP2R1b/pP1p1PpR/Pp4P1/1P6/1K1P4/8}
The solution is more or less self-explanatory. Black is stalemated apart from his d-pawn, so White has two free moves before he has to worry about releasing the stalemate. On the other hand, it is hard to envisage a mating position since Black's king is virtually surrounded by his own pieces. The key idea is to leave the rook on f6 undefended at the right moment, forcing ...Kxf6, and then mate with the bishop along the long diagonal. The problem is that in the diagram the bishop has no useful moves because the four enemy pawns on the queenside prevent the bishop moving to d6, c5 or b4.]

78.
[{B:n1N3br/2p1Bpkr/1pP2R1b/pP1p1PpR/Pp4P1/1P6/1K1P4/8}
{S:h5h1}
1 Rh1!
A mysterious rook move.]

79.
[{S:d5d4}
1...d4]

80.
[{S:h1a1}
2 Ra1!!
The mystery deepens. Why has White sent his rook to the furthest corner of the board when he is trying to mate the black king?]

81.
[{S:d4d3}
2...d3
Black's pawn moves are exhausted and now White must lift the stalemate.]

82.
[{S:a1a3}
3 Ra3!
This is the point of White's rook maneuver. White unblocks the queenside pawn structure and opens the diagonal for his bishop.]

83.
[{S:b4a3}
3...bxa3+]

84.
[{S:b2a1}
4 Ka1
Of course not 4 Ka2? stalemate.]

85.
[{S:a3a2}
4...a2
Everything is in place for the decisive maneuver, which involves the sacrifice of White's other rook.]

86.
[{S:e7a3}
5 Ba3!]

87.
[{S:g7f6}
5...Kxf6
All Black's moves are absolutely forced.]

88.
[{S:a3b2}
6 Bb2 mate]

89.
[{B:b1B1Q3/pr6/k7/P6p/1P6/2P2q2/1K6/8}
{V:This is quite a tricky problem, but that should not put you off tackling it. Although it is given as a mate in eight, the play is more like that of an endgame study (indeed, the composer Rusinek is best known as a world-class study expert). The wonderful solution is certainly a worthwhile reward for those who do persevere. White to play and mate in eight. Try your move on the board.;c3c4;Correct;Incorrect.;It isn't giving too much away to say that the first move is 1 c4 (threatening mate on b5) and that Black responds by 1...Qf6+. Then White's immediate ambition is to avoid perpetual check. His method of doing this is spectacular and unexpected.}]

90.
[{B:b1B1Q3/pr6/k7/P6p/1P6/2P2q2/1K6/8}
White is a rook down, so his only hope of winning, let alone giving mate in eight, is to exploit the precarious position of Black's king. It is true that White can win Black's queen by 1 Qe5 Qd1 2 Qe6+ Kb5 3 Qe8+ Kc4 4 Be6+ Kd3 5 Qd8+, but this line certainly isn't going to lead to mate in eight. The above line is typical, however, in that White's attacking attempts don't lead to mate because Black's king slips out via b5. This is the basis for White's first move.]

91.
[{S:c3c4}
1 c4!
In addition to covering b5, this sets up the deadly threats of 2 Qb5 mate and 2 Qe6 (or g6)+. There is also a potential mate by Qc6, and it is obvious that Black's queen can't cover all these squares. It follows that Black's only hope is to try for perpetual check.]

92.
[{S:f3f6}
1...Qf6+
The best attempt 1...Qf2+ and 1...Qg2+ are both met by 2 Ka3!, when Black has nothing better than 2...Qf3+ transposing into the main line, but with White having saved a move.]

93.
[{S:b2a2}
2 Ka2!
Care is required. White's king would like to head towards a4, but 2 Ka3? allows a check on c3. We shall see in a moment why 2 Kb3? Qf3+ is bad.]

94.
[{S:f6f2}
2...Qf2+
The only chance, since the desperate 2...Qb6 is refuted by 3 axb6 Kxb6 4 Qe5 with mate in at most two more moves.]

95.
[{S:a2a3}
3 Ka3!]

96.
[{S:f2f3}
3...Qf3+
Certainly not 3...Qg3+? 4 Ka4 with a quick mate. Now, however, White appears to have arrived at a dead end since the obvious 4 Ka4 is met by 4...Qd1+ 5 Ka3 Qa1+ and the checks can't be avoided. Other king moves are met by ...Qf2+ and White is not making progress. If you have not found the whole solution, this is a good moment to stop and figure out what comes next.]

97.
[{S:e8e3}
4 Qe3!!
A truly incredible move. Already a rook down, White offers his queen with check. But if Black accepts, then 4...Qxe3+ 5 Ka4 leaves him in an impossible position. The threat is 6 b5 mate, and Black can only delay the end temporarily by 5...Qb3+ 6 Kxb3 h4 7 Ka4 h3 8 b5 mate. Therefore Black has to decline the sacrifice and move his queen away. However, Black has achieved some success. White's queen is not so actively placed on e3, and instead of threatening four different mates White's only threats are Qe6 and Qh6. Black can just about cover both squares. Incidentally, we can now see why 2 Kb3? Qf3+ would have been bad; the trick with Qe3 doesn't work when White's king is on b3, because Black simply ignores the offered queen and plays ...Qd1+.]

98.
[{S:f3f6}
4...Qf6
Not only preventing a queen mate, but also setting up a counter-threat of 5...Qa1+. Once again it is worth stopping to think about White's next move.]

99.
[{S:e3h6}
5 Qh6!!
The same idea again, but this time Black's queen is pinned, so he has no choice about accepting the queen sacrifice. If Black had played 4...Qc6, then White's reply would have been the same.]

100.
[{S:f6h6}
5...Qxh6
Now that Black has been deprived of his check on a1, the white king can close in for the kill.]

101.
[{S:a3a4}
6 Ka4]

102.
[{S:h6c6}
6...Qc6+
There is no defense to the deadly threat of b5 mate. Black can only delay
the end by one move.]

103.
[{S:b4b5}
7 b5+]

104.
[{S:c6b5}
7...Qxb5+]

105.
[{S:c4b5}
8 cxb5 mate.]

106.
[{B:3K1B2/1p6/pp6/rk2N3/b1p5/1pP5/1P2P3/8}
{V:Very long problems may appear intimidating, but in fact they are often quite easy to solve. Usually Black is completely tied up and White can plan long-range maneuvers without worrying too much about enemy counter-play. This is a case in point, White cannot afford to let Black's rook and bishop out of the box, so he must restrict Black to king moves throughout the solution. White to play and mate in 20.;d8e7;Correct;Incorrect.;Long problems can often be solved by making a wish and then seeing how the wish can be made to come true. In this position White could mate in two by 1 Nf3 Kc6 2 Nd4 mate, if only the d5-square were covered. So White's wish is to have his e-pawn on e4. It takes 18 moves for the wish to become reality, but all Black's moves are forced, which makes life much easier for White.}]

107.
[{B:3K1B2/1p6/pp6/rk2N3/b1p5/1pP5/1P2P3/8}
Such long problems have a peculiar logic all their own. White's ultimate aim is to mate by Nf3 and Nd4 mate, but at the moment 1 Nf3 Kc6 2 Nd4+ fails to 2...Kd5, so first of all White must advance his e-pawn to e4 with gain of tempo. This large problem can be broken down into smaller sub-problems. White would like to maneuver with his bishop, for example by 1 Bh6 Kc5 2 Be3+, but once again Black's king escapes via d5. So the first step is to put a temporary guard on d5 to free the bishop.]

108.
[{S:d8e7}
1 Ke7]

109.
[{S:b5c5}
1...Kc5]

110.
[{S:e7e6}
2 Ke6+]

111.
[{S:c5b5}
2...Kb5
Although d5 is now guarded, White cannot yet mate by 3 Nf3 Kc6 4 Nd4+ because he has given up control of c7. d5 has to be covered by the e-pawn if this mating idea is to work, but that is still a long way off.]

112.
[{S:f8h6}
3 Bh6]

113.
[{S:b5c5}
3...Kc5
Black's moves are forced throughout the solution.]

114.
[{S:h6e3}
4 Be3+]

115.
[{S:c5b5}
4...Kb5
White is now free to maneuver with his bishop, but it isn't obvious how this helps to advance the e-pawn. The key idea is to transfer the bishop to f2 with gain of tempo, then e2-e3 will lift the stalemate, forcing ...Kc5, and after e3-e4+ White's wish has been granted.]

116.
[{S:e3g5}
5 Bg5
The bishop couldn't transfer from f8 to f2 directly, because the f8-h6 diagonal wasn't long enough. Once again a tricky problem can be broken down into smaller problems, first transfer the bishop to the d8-h4 diagonal, and then use the h4 square to reach f2.]

117.
[{S:b5c5}
5...Kc5]

118.
[
{S:g5e7}
6 Be7+]

119.
[{S:c5b5}
6...Kb5]

120.
[
{S:e7h4}
7 Bh4]

121.
[
{S:b5c5}
7...Kc5]

122.
[
{S:h4f2}
8 Bf2+]

123.
[
{S:c5b5}
8...Kb5
At long last the e-pawn can make its first step forward.]

124.
[
{S:e2e3}
9 e3]

125.
[{S:b5c5}
9...Kc5]

126.
[{S:e3e4}
10 e4+]

127.
[
{S:c5b5}
10...Kb5
The e-pawn has reached its final destination, but White's king and bishop are on the wrong squares for the final mating idea. The next step is to execute all the previous maneuvers in reverse. First of all the bishop has to return to f8.]

128.
[
{S:f2h4}
11 Bh4]

129.
[
{S:b5c5}
11...Kc5]

130.
[
{S:h4e7}
12 Be7+]

131.
[
{S:c5b5}
12...Kb5]

132.
[
{S:e7g5}
13 Bg5]

133.
[
{S:b5c5}
13...Kc5]

134.
[
{S:g5e3}
14 Be3+]

135.
[
{S:c5b5}
14...Kb5]

136.
[
{S:e3h6}
{S:b5c5}
15 Bh6  Kc5]

137.
[
{S:h6f8}
16 Bf8+]

138.
[
{S:c5b5}
16...Kb5
Now White's initial king maneuver can be reversed.]

139.
[
{S:e6e7}
17 Ke7]

140.
[
{S:b5c5}
17...Kc5]

141.
[
{S:e7d8}
18 Kd8+]

142.
[
{S:c5b5}
18..Kb5
The king controls c7 and the pawn controls d5, so the stage is set for the final act.]

143.
[
{S:e5f3}
19 Nf3]

144.
[
{S:b5c6}
19...Kc6]

145.
[
{S:f3d4}
20 Nd4 mate.]

146.
[
{F:B}{B:6R1/7q/8/5k2/3K1B2/8/8/8}
Since this is the first helpmate, here are a few words of explanation to those who are new to this type of puzzle. In a helpmate, both sides cooperate to help White mate Black. While this idea may seem slightly bizarre, helpmates are favorites of many over-the-board players, perhaps because normally they can only dream of such a cooperative opponent! It is a convention of helpmates that Black moves first, so in this puzzle both sides make three moves and White's final move delivers mate. Although Black is helping White, all the moves must be legal.The first few helpmates are quite easy, so there is no need to be afraid!]

147.
[
{F:B}{B:6R1/7q/8/5k2/3K1B2/8/8/8 BLACK}
{V:Black to play, helpmate in three. Try your solution on the board.;f5f6;Correct;Incorrect.;The key to any helpmate is to spot the mating position. Once this has been accomplished, it is normally not to hard to find the sequence of moves which leads to the mate. In this position try to visualize a mating position with the given material, and then see if it can be reached in three moves. It is easier to mate a king on the edge of the board than in the center, and it is easier still in the corner!}]

148.
[
{F:B}{B:6R1/7q/8/5k2/3K1B2/8/8/8}
It is possible to mate in the center of the board with the given material (for example, with the bishop on h4, king on d5 and rook on f6 against a king on f5 and queen on g4), but it doesn't take long to see that such a mating position requires more than three white moves to set up. Mating on the edge of the board is more tempting, because then mate can be arranged without the participation of White's king. Once again, however, the time element proves an insurmountable problem. The final possibility is to mate in the corner, which here implies h8 since that is the only corner which Black can reach in three moves. It also means that Black has no time to move his queen. A corner mate requires a double check, and now we need only work out how to temporarily block off White's pieces to allow Black's king to actually move into the corner. The method is pleasantly geometrical.]

149.
[
{S:f5f6}
1...Kf6]

150.
[
{S:g8a8}
2 Ra8]

151.
[
{S:f6g7}
2...Kg7]

152.
[
{S:f4b8}
3 Bb8]

153.
[
{S:g7h8}
3...Kh8]

154.
[
{S:b8e5}
4 Be5   mate
Although the last move is numbered '4', it is actually White's third move of the solution, justifying the stipulation 'helpmate in three'.]

155.
[
{F:B}{B:8/8/8/8/1k6/8/7q/R2NK3 BLACK}
{V:Remember that Black moves first in a helpmate, so here both sides play three moves, cooperating so as to help White mate Black. Black to move, helpmate in three.;h2b8;Correct;Incorrect.;The position of the king on e1 and the rook on a1 is bit of a give away, in a problem this almost always means that castling is involved  in the solution (although a few composers are fond of red herrings...). In helpmates, finding the mating position is 90% of the battle, so here you need to look for a mating position with White's king on c1.}]

156.
[
{F:B}{B:8/8/8/8/1k6/8/7q/R2NK3}
The position of the rook and king strongly suggests that White's first two moves will be a knight move followed by 0-0-0. Since it is not possible to mate with the rook on d1, the third and final move will be with the rook. It follows that White arrives at the mating position by Nb2, 0-0-0 and Rd3, with Black's queen on b4. One Black move is consumed by ...Kc3, which leaves two moves for Black's queen to reach b4. At first it seems that there are several possible routes for the queen, for example via b2, f4, h4, d6 or b8, but it turns out that only one of these works. Black cannot play 1...Qb2 because White's knight needs to move to b2, 1...Qh4+ delivers check and so prevents castling, while 1...Qd6 (1...Qf4 is the same) 2 Nb2 Kc3 3 0-0-0?? is illegal. So the only way is ...]

157.
[
{S:h2b8}
1 ...Qb8!]

158.
[
{S:d1b2}
2 Nb2]

159.
[
{S:b4c3}
2...Kc3]

160.
[
{S:a1d1}{S:e1c1}
3 0-0-0]

161.
[
{S:b8b4}
3...Qb4]

162.
[
{S:d1d3}
4 Rd3 mate.
When showing someone this problem, a good trick is to say '... and this is White's side of the board, but of course it doesn't matter since there aren't any pawns'.]

163.
[
{F:B}{B:K7/2q2n2/3n2kB/6P1/5P2/6P1/7b/8 BLACK}
{V:Black to move, helpmate in three. Try it on the board.;f7e5;Correct;Incorrect.;If only h7 were blocked and the knight on d6 moved away, then White could mate by g4 and f5. At first sight, the problem can be solved by playing the knight on d6 to h7, but after 1...Ne4 2 g4 Nf6 White has no pass move and is forced to destroy the mate by moving the bishop. The solution is to find a way of blocking h7 with a different black piece, in such a way as to give White a waiting move.}]

164.
[
{F:B}{B:K7/2q2n2/3n2kB/6P1/5P2/6P1/7b/8}
This problem is a study in tempo-play. White would like to mate by g4 and f5, but for this the knight on d6 has to move away and the square h7 must be blocked. The natural idea is to combine both of these in a single plan, by transferring the d6-knight to h7. This fails because after 1...Ne4 2 g4 Nf6 White is forced to move the bishop, and this disrupts the mating net. White will always require a waiting move, and this can only be with the king. It follows that Black's queen will have to move, and so the second idea is to use the queen to block h7. Of course, we mustn't forget about moving the knight on d6, but it is possible to combine both plans by moving the knight on f7, playing ...Qh7, and then playing the knight on d6 to f7. The only problem is that 1...Nh8 2 g4 Qh7 3 Kb8 Ndf7 pins the pawn on f4, and so White cannot deliver mate. This explains why the f7-knight must choose the right destination on the first move...]

165.
[
{S:f7e5}
1...Ne5
All the other pieces are going to move off the h2-b8 diagonal, so Black must prepare to unpin the f4-pawn.]

166.
[
{S:g3g4}
2 g4]

167.
[
{S:c7h7}
2...Qh7]

168.
[
{S:a8b8}
3 Kb8]

169.
[
{S:e5f7}
3...Nf7]

170.
[
{S:f4f5}
4 f5  mate.]

171.
[
{F:B}{B:1q6/3r1nn/3b2b1/2Q1kr2/2R2P2/3K4/6B1/8}
One criticism of helpmates is that because variations are impossible, the solutions lack the variety shown in other types of problems. One way around this is to have more than one solution, as the French composer Caillaud has done here. In most problems an unintended second solution is held to be a fatal flaw destroying the value of the problem, but helpmates with intentional multiple solutions are an exception to the rule. It is important that the solutions be closely related to each other, very often one line will echo the strategy of the other. For this reason, once you have found one solution to a helpmate, finding the others is normally quite easy.]

172.
[
Problem composers love paradox, and this problem is no exception. What is especially paradoxical in a helpmate? The answer is the sacrifice of white material. Normally, a sacrifice is made to force the opponent to do something he doesn't want to do, but when he is cooperating in any case, sacrifices appear to lose their point. Indeed, at first it is hard to see any reason why a reduction in White's material can possibly help him.]

173.
[
White's force is quite substantial, and it is amazing that there aren't hundreds of ways of contriving a mate with queen, rook and bishop. Curiously enough, it is the very power of White's force which makes it hard. For example if the queen weren't there, 1 any 2 Re4+ Kd5 3 Re5 would be mate, or if the bishop disappeared, then 1 any 2 Qe3+ Kd5 3 Qe4 would do the trick. This leads to the idea of sacrificing white material, and you might expect that if a composer was arranging a sacrifice, he wouldn't be satisfied with anything less than the queen.]

174.
[
But why should White sacrifice his queen rather than simply move it out of the way? Now the element of imagination enters. One answer might be that Black's first move gives check, so that White has no time to quietly withdraw the queen. Now we have a chance of spotting a solution...]

175.
[{F:B}{B:1q6/3r1nn1/3bk1b1/2Q2r2/2R2P2/3K4/6B1/8 BLACK}
{V:Can you find the two solutions? Try it on the board. Black to move. Helpmate in two, two solutions.;f5f6;Correct;Incorrect.;You should not be afraid to sacrifice some white material in order to force mate.}]

176.
[
{S:f5f6}
1...Rf6+]

177.
[
{S:c5f5}
2 Qf5+]

178.
[
{S:e6f5}
2...Kxf5]

179.
[
{S:g2h3}
3 Bh3 mate]

180.
[
{F:B}{B:1q6/3r1nn1/3bk1b1/2Q2r2/2R2P2/3K4/6B1/8}
The second solution almost certainly embodies identical strategy, i.e. Black's first move is a discovered check, and White's reply sacrifices the queen on the square Black has just vacated. This leads us naturally to the d6-bishop, and the second solution is...]

181.
[
{S:d6e7}
1...Be7+]

182.
[
{S:c5d6}
2 Qd6+]

183.
[
{S:e6d6}
2...Kxd6]

184.
[
{S:c4c6}
3 Rc6 mate]

185.
[
{F:B}{B:8/8/8/7K/1k6/3P1Rp1/8/6B1 BLACK}
{V:In longer helpmates, it is even more important to start by finding the mating position. The astronomical number of possibilities means that although a trial and error approach might work for a computer, the human has to proceed by using a combination of logic, intuition and experience. Black to move. Helpmate in 4. Try your solution on the board.;b4c3;That's the right one!;Incorrect.;It isn't hard to see that White cannot mate the black king on the queenside, the rook and bishop simply aren't up to the job by themselves. In other words, the black king has to head for the kingside, where White's own king can lend a hand.}]

186.
[
{F:B}{B:8/8/8/7K/1k6/3P1Rp1/8/6B1}
This problem is relatively easy to solve, because there is only one plausible mating position, with Black's king on f4, the white bishop on d4 and his rook on the f-file. It takes Black's king four moves to reach f4, and since c4 and c5 are covered, the first move must be ...]

187.
[
{S:b4c3}
1...Kc3
Black's king must reach f4 via either e3 or e5. But if Black's last move is ...Ke3-f4, then White's bishop cannot have been on d4 the move before, in other words White's last move must be Bd4, giving mate by discovery. The bishop cannot have come from f2 (because Black's king was on e3), so it must have come from f6, but there isn't enough time for White to reach f6, for example 2 Rf8 Kd2 3 Bd4 Ke3?? 4 Bf6 Kf4 5 Bd4 would be a solution, except for the illegal move in the middle. Therefore Black's king must go via d4 and e5, so White's second move must be Re3 or Rf2. Now it doesn't take long to find the solution.]

188.
[
{S:f3f2}
2  Rf2
First the rook blocks the bishop ...]

189.
[
{S:c3d4}
2...Kd4]

190.
[
{S:f2f1}
3 Rf1+]

191.
[
{S:d4e5}
3...Ke5]

192.
[
{S:g1f2}
4 Bf2
... and then the bishop blocks the rook.]

193.
[
{S:e5f4}
4...Kf4]

194.
[
{S:f2d4}
5 Bd4 mate.]

195.
[
{F:B}{B:8/8/8/8/4kpP1/2K1b3/3P2r1/7B BLACK}
{V:This is one of my own compositions. Several grandmasters have been completely stumped by it, but GM Kindermann solved it in ten minutes, and anyone who beats his time (without looking at the hint!) should consider themselves expert solvers. Black to move. Helpmate in 4.;e4e5;Correct;Incorrect.;It may help if I reveal that I have a fondness for geometrical themes. It is also worth noting that White could mate by d4 and Bxg2, except for the annoying pawn which can interpose on f3. If only the bishop could get round to the other side of the king, then Black wouldn't have this defense.}]

196.
[
{F:B}{B:8/8/8/8/4kpP1/2K1b3/3P2r1/7B} 
This is a really tough problem, firstly because the mating position is not at all obvious, and secondly because there are a lot of near-misses, i.e. mating positions which could, theoretically, be reached in four moves, but fail for reasons of move-order. One example is 1...Bd4+ 2 Kc2 Kd3?? 3 Kd1 Re2 4 Bc6 Re4 5 Bb5 mate, although this takes four moves, there is no move-order without an illegal move in the middle.]

197.
[
{F:B}{B:8/8/8/8/4kpP1/2K1b3/3P2r1/7B}
Curiously, the actual mating position is perhaps the most obvious one - White plays d4 and mates with his bishop on the long diagonal. In order to avoid the defense ...f3, the bishop must deliver mate from the other side of the black king. At first sight this is impossible, because a maneuver such as Bg2-f1-a6-b7 takes four moves, leaving no time for d4. But this is where the geometry comes in ...]

198.
[
{S:e4e5}
1... Ke5
Black is going to need his rook, so the first move is to unpin it.]

199.
[
{S:d2d3}
2 d3
This point of this is to clear the second rank for the rook.]

200.
[
{S:g2b2}
2...Rb2
Black frees the bishop ...]

201.
[
{S:h1a8}
3 Ba8]

202.
[
{S:b2b7}
3...Rb7
... only to rebury it in the opposite corner. The idea is to block White's control of the long diagonal long enough to let the black king reoccupy
e4.]

203.
[
{S:d3d4}
4 d4+]

204.
[
{S:e5e4}
4...Ke4]

205.
[
{S:a8b7}
5 Bxb7 mate.]

206.
[
{F:B}{B:8/8/2k5/4b2n/p7/pp6/rp5P/1K1n4 BLACK}
{V:In this problem, White's pawn sets off on mission impossible to single-handedly deliver mate. Black to move. Helpmate in eight.;e5h8;Correct;Incorrect.;White's king is totally imprisoned, so the h-pawn has to do all the work. The pawn can promote in five moves, presumably to a queen (a knight is worth a thought, but there is no mating position which can be reached in time). There is no mating position with a queen against just the king and minor pieces, so somehow the rook must be brought into the game ...}]

207.
[
White's pawn will promote in five moves, leaving just three to arrange the mate. No mate is possible in eight moves if White promotes to a knight, so we can assume that White will promote to a queen. Even so, no mating position is possible using just the black king and minor pieces. A mate is possible on the queenside, by playing Qxa3 and then marching Black's king in to a3, but this takes too long. The conclusion is that White has to bring the rook into the game. Fortunately, this is quite easy, because after promoting on h8 White can play Qxb2.]

208.
[
This is already White's sixth move, however, so White's seventh move will be to move the queen away. Black must then move his rook in such a way as to allow immediate mate. There are only two possibilities, either Black's king is on d1, when ...Rd2 will allow Qf1 mate, or Black's king is on h1, when ...Rh2 will again allow Qf1 mate. The first scheme fails because of the time element, if we add up Black's moves we find that playing the king to d1 takes five, the knight on d1 must move, the knight on h5 must move to allow the pawn to promote and the bishop on e5 must move to allow Qh8xb2, adding up to nine moves.]

209.
[
Thus the mate must be on h1. The last moves will be Qxb2 and Qf6 by White, allowing ...Rh2 and then Qf1 mate. Playing the king to h1 and ...Rh2 is six moves, and as before the h5-knight and bishop must move, so this plan is just possible. Now the problems start to appear. Where can the h5-knight move? Going to f6 or g7 blocks Qh8xb2, ...Ng3 stops the mate and ...Nf4 blocks Qf6-f1. It has been possible to proceed this far by logic alone, but logic can only take you so far, and then inspiration has to take over. It turns out that the only solution is for the h5-knight to be captured by the white pawn, but since the pawn must promote on h8, the bishop has to join the knight in a suicide pact.]

210.
[
{S:e5h8}
1...Bh8!!
The knight has to make way for the pawn, so this move must come right away.]

211.
[
{S:h2h4}
2 h4]

212.
[
{S:h5g7}
2...Ng7
Now everything is ready for h6xg7 and g7xh8.]

213.
[
{S:h4h5}
3 h5]

214.
[
{S:c6d5}
3...Kd5]

215.
[
{S:h5h6}
4 h6]

216.
[
{S:d5e4}
4...Ke4]

217.
[
{S:h6g7}
5 hxg7]

218.
[
{S:e4f3}
5...Kf3]

219.
[
{S:g7h8}{X:h8}{P:WQh8}
6 gxh8Q
Now that the knight and bishop have self-destructed, the decks are clear for the white queen.]

220.
[
{S:f3g2}
6...Kg2]

221.
[
{S:h8b2}
7 Qxb2+]

222.
[
{S:g2h1}
7...Kh1]

223.
[
{S:b2f6}
8 Qf6]

224.
[
{S:a2h2}
8...Rh2]

225.
[
{S:f6f1}
9 Qf1 mate.]

226.
[
{F:W}{B:6K1/R7/8/8/8/3b2k1/3P3p/8}
This is the first of the endgame studies. There are two possible conditions for a study, either 'White to play and win' or 'White to play and draw'. The number of moves is not given because often there is no clear-cut finish, as with a problem. The solution ends when the result is obvious, this can be because of mate or stalemate, but more often it is because a theoretically winning (or drawing) material balance has been reached. The situation is similar to an over-the-board game, except that in a study you know that the win or draw is there if you look hard enough, whereas in a game you can only hope.]

227.
[
{V:Kozlowski's study is a simple introduction. Black's passed pawn is on the verge of promotion, but there is a way for White to counteract it. Find the move that's leads to a draw. White to play and draw.;a7a1;Correct;Incorrect.;The key position arises after 1 Ra1 Kg2. Black threatens 2...Bf1 followed by ...h1Q, but White has one spare move with which to improve his king position... }]

228.
[
{S:a7a1}
1 Ra1
This is forced. After 1 Rg7+? Kf2 2 Rf7+ Ke2 3 Re7+ Kxd2 White cannot stop the pawn promoting, while 1 Ra3? h1Q 2 Rxd3+ Kf2 is a theoretical loss (positions with a queen against a rook and a pawn can only be drawn if the defender's king is near the pawn, or if the pawn is far advanced).]

229.
[
{S:g3g2}
1...Kg2
Black intends to block the rook by ...Bf1, and then promote his pawn. This is the key moment, so you might like to think about White's next move.]

230.
[
{S:g8h8}
2 Kh8!!
The drawing idea is to answer ...Bf1 by Ra7, intending to trap the newly-created queen by Rh7. Simply waiting doesn't work, for example 2 Rc1? Bf1 3 Rc7 h1Q 4 Rh7 Bc4+ and the queen escapes along the first rank. The problem in this line is that Black has a bishop check, so White must move his king to a dark square, while at the same time retaining control of a square on the h-file. 2 Kg7? Bf1 3 Ra8 h1Q 4 Rh8 doesn't work because of 4...Qg1 and White's king blocks the g-file. The only solution is to play the king to h8, even though it goes against one's natural instincts to allow Black to promote with check.]

231.
[
{S:d3f1}
2...Bf1]

232.
[
{S:a1a7}
3 Ra7!]

233.
[
{S:h2h1}{X:h1}{P:BQh1}
3...h1Q+
After 3...Bd3 White simply returns to a1.]

234.
[
{S:a7h7}
4 Rh7]

235.
[
{S:h1g1}
4...Qg1]

236.
[
{S:h7g7}
5 Rg7+  ...winning the queen and drawing.]

237.
[
{B:1B6/8/7P/4p3/3b3k/8/8/2K5}
{V:In this study it is White who has a dangerous passed pawn. How can White usher the pawn through to promotion? Win with white moving first. Try to do it on the board.;b8a7;Correct;Incorrect.;If Black can safely play ...e4, then the position will be a draw because his bishop will hold up the pawn long enough for the black king to round it up. White's one and only priority is to prevent ...e4 and he shouldn't shrink from unconventional methods to achieve this aim.}]

238.
[
The battle revolves around whether or not Black manages to play ...e4. If he succeeds, then the h-pawn is stopped and Black's king will be able to deal with the pawn. The first few moves of the study are quite easy, because White has only one reasonable way to prevent Black's ...e4.]

239.
[
{S:b8a7}
1 Ba7!]

240.
[
{S:d4a1}
1...Ba1
Black must decline the sacrifice, because after 1...Bxa7 2 h7 the pawn runs home. If Black plays 1...Bc3, then 2 Kc2 transposes into the main line.]

241.
[
{S:c1b1}
2 Kb1]

242.
[
{S:a1c3}
2...Bc3]

243.
[
{S:b1c2}
3 Kc2]

244.
[
{S:c3a1}
3...Ba1
Black's moves are forced. White has transferred his king from c1 to c2 with gain of tempo, but now he appears to be at a dead end, since after 4 Kd3 Black just plays 4...e4+ 5 Kxe4 Kh5, with an easy draw. In all the best studies, there comes a moment when it seems utterly impossible for White to reach his target. This is usually the point at which the composer has hidden his main idea.]

245.
[
{S:a7d4}
4 Bd4!!
An amazing double bishop sacrifice. After 4...exd4, Black's pawn has been deflected one square closer to White's king, allowing the reply 5 Kd3 sealing the diagonal shut, followed by 6 h7.]

246.
[
{S:a1d4}
4...Bxd4
Taking the bishop this way doesn't help.]

247.
[
{S:c2d3}
5 Kd3
Now Black cannot play 5...e4+ because his bishop is vulnerable on d4, so White gains a vital tempo to block the diagonal.]

248.
[
{S:d4a1}
5...Ba1]

249.
[
{S:d3e4}
6 Ke4
...followed by 7 h7 and 8 h8Q.]

250.
[
{B:r7/8/8/8/8/2R5/n7/Nn1K1k2}
{V:In order to win an ending without pawns, it is usually not enough to be a minor piece up. It follows that the material balance in the diagram should lead to a draw, but White's problem is that his rook is under attack, and after it moves Black will play ...Nac3+ winning the knight on a1. Two extra pieces is certainly enough to win, unless there is an immediate draw for some reason. Find white's move that leads to a draw.;c3f3;Correct;Incorrect.;The clue is the last sentence in the question. White has to find a way to lose his knight in such a way as to set up a tactical defense. Remember than a king and two knights cannot win against a lone king, so if the rooks were exchanged ...}]

251.
[
{B:r7/8/8/8/8/2R5/n7/Nn1K1k2}
It is essential to drive the king further away before doing anything else, since 1 Rc2?, for example, is met by 1...Rd8+ and mate next move.]

252.
[
{S:c3f3}
1 Rf3+!]

253.
[
{S:f1g2}
1...Kg2
Black must keep up the attack on White's rook. After the tame 1...Kg1, White rescues his knight with 2 Nb3 and Black has no special tricks, so the position is drawn.]

254.
[
{S:f3b3}
2 Rb3!
White's drawing idea depends on a lateral check, and this is the only way for the rook to reach the second rank. It also explains why the immediate 1 Rb3? wouldn't have worked.]

255.
[
{S:a2c3}
2...Nc3+
Black continues with his plan.]

256.
[
{S:d1c1}
3 Kc1!]

257.
[
{S:a8a1}
3...Rxa1]

258.
[
{S:b3b2}
4 Rb2+]

259.
[
{S:g2g1}
4...Kg1
It doesn't make any difference where Black moves his king. The critical moment has arrived, so this is your last chance to spot the spectacular drawing idea.]

260.
[
{S:b2a2}
5 Ra2!!
An incredible double rook offer. If Black plays 5...Rxa2 then White is stalemated, so in order to avoid losing his own rook Black has to play ...]

261.
[
{S:c3a2}
5...Nxa2+]

262.
[
{S:c1b2}
6 Kb2
A visual position. Black's poor rook is caught in the deadly embrace of the black knights, White will take the rook next move, giving rise to the drawn ending of king and two knights v king.]

263.
[
{B:8/8/7q/8/1Q2Nk2/5p2/8/3bK1b1}
{V:White is way down on material, so only mate or winning Black's queen will tilt the balance in his favor. This study is just pure tactics from beginning to end, so it is a good test of your tactical ability to solve it from the diagram, without moving the pieces. White to play and win.;e4d6;Correct;Incorrect.;The right choice of first move leads to the rapid capture of Black's queen, but enemy counter-play soon restores the balance. Despite this, it is White who has the last word.}]

264.
[
The first move is quite easy, because it ensures that White can fork king and queen the following move. Indeed, it seems so strong that at first it is hard to see how Black can play on.]

265.
[
{S:e4d6}
1 Nd6+!]

266.
[
{S:f4g3}
1...Kg3
Black cannot avoid either Nf7+ or Nf5+ next move, so he can kiss his queen goodbye, but it takes time for White to take on h6 and Black can use this to develop counter-play using his advanced pawn.]

267.
[
{S:d6f5}
2 Nf5+]

268.
[
{S:g3g2}
2...Kg2
Suddenly problems start to appear for White. The immediate capture on h6 is met by ...f2+ and ...f1Q, when Black restores the material balance and draws. So White must give a preliminary check.]

269.
[
{S:b4g4}
3 Qg4+]

270.
[
{S:g2h1}
3...Kh1
Forced, because 3...Kh2 allows 4 Qg3+ Kh1 5 Nxh6 and White takes the queen in safety. After the move played White has no queen check, while taking on h6 allows ...f2+ followed by ...Bxg4. If you have not already seen the finish, now is the time to stop and work it out for yourself.]

271.
[
{S:f5h6}
4 Nxh6!
This unexpectedly succeeds, even though Black can regain the queen.]

272.
[
{S:f3f2}
4...f2+]

273.
[
{S:e1f1}
5 Kf1]

274.
[
{S:d1g4}
5...Bxg4]

275.
[
{S:h6g4}
6 Nxg4
Black has but one legal move ...]

276.
[
{S:g1h2}
6...Bh2
... which allows mate in one.]

277.
[
{S:g4f2}
7 Nxf2 mate.]

278.
[
{B:8/3k4/1K6/8/4BR2/4p3/4p3/8}
{V:Play white first. Find the move that leads to a win.;e4f5;Correct;Incorrect.;White has a large material advantage, but Black's e-pawn is about to promote. It is possible to stop Black's pawn after either bishop check, but one of the two checks allows Black to spring a diabolical trap. Black can lay the same pitfall after the other check, but this time there is a cunning refutation. Which one is correct?}]

279.
[
The most obvious move is 1 Bc6+?, because after a couple of checks White can take the e3-pawn with his rook. Unfortunately, this doesn't win because after 1...Ke6 2 Re4+ Kd6 3 Rxe3 e1Q 4 Rxe1 Black is stalemated. The solution starts with the other bishop check.]

280.
[
{S:e4f5}
1 Bf5+!]

281.
[
{S:d7d6}
1...Kd6 (or d8)
1...Ke7 2 Re4+ transposes to the main line.]

282.
[
{S:f4d4}
2 Rd4+]

283.
[
{S:d6e7}
2...Ke7
After 2...Ke5 3 Re4+ Kxf5 4 Rxe3 White wins with his extra rook.]

284.
[
{S:d4e4}
3 Re4+]

285.
[
{S:e7d8}
3...Kd8
Black again attempts to force stalemate, this time by 4 Rxe3 e1Q 5 Rxe1. White's next move avoids the trap and forms the main point of the study.]

286.
[
{S:f5d7}
4 Bd7!!
Amazingly, White makes no attempt to stop Black queening.]

287.
[
{S:e2e1}{X:e1}{P:BQe1}
4...e1Q
Black has no choice, since otherwise Rxe3 wins.]

288.
[
{S:d7b5}
5 Bb5!
Suddenly the trapper has been trapped himself. By blocking the b-file, the bishop has cut out any checks from Black's queen, and there is now no way of preventing mate by Re8.]

289.
[
{B:1N6/8/K7/3k4/3p3B/p7/2PP4/8}
{V:White to play and win.  Try it on the oard.;b8c6;Correct;Incorrect.;In an over-the-board game, the great majority of moves are made without the end of the game being foreseen. A similar attitude is often helpful when solving studies, just try the move that looks best, and see where it leads. In this position, White is well up on material, but Black's advanced a-pawn is on the verge of promotion. Why not use the out-of-play knight to delay the advance of the pawn, and see what turns up?}]

290.
[
The knight sacrifices itself for the sake of a tempo. Using the bishop for same purpose is ineffective, for example 1 Bf6 a2 2 Bxd4 Kxd4 3 Nc6+ Ke4 and White cannot stop the pawn.]

291.
[
{S:b8c6}
1 Nc6!]

292.
[
{S:d5c6}
1...Kxc6
Black must accept, because after 1...a2 2 Nb4+ he loses his only hope.]

293.
[
{S:h4f6}
2 Bf6
Attacking the undefended pawn on d4 holds Black up for another move.]

294.
[
{S:c6d5}
2...Kd5]

295.
[
{B:16/K4B2/3k4/3p4/p7/2PP4/8}
{V:Once again Black's reply is forced, as after 2...Kc5 3 Be7+ he loses the pawn. What is the next step in White's struggle against the a-pawn?;d2d3;Correct;Incorrect.;At first sight White's efforts have achieved little, and he now faces exactly the same problem as in the initial position, only with a knight less. But the position of the bishop on the long diagonal is a new factor, for example if White advances his c-pawn, then ...dxc3 can be met by Bxc3 stopping the a-pawn. How should White prepare the c-pawn push?}]

296.
[
{S:d2d3}
3 d3
White wants to play c4+ without allowing the reply ...Kxc4.]

297.
[
{S:a3a2}
3...a2
The only move. Black's king must guard d4, and 3...Kc5 still loses to 4 Be7+.]

298.
[
{S:c2c4}
4 c4+]

299.
[
{S:d5c5}
4...Kc5
After 4...dxc3 5 Bxc3 White wins by bringing his king back to support his own d-pawn. Now we are at the climax of the study. Black's a-pawn is about to promote with check, but it turns out that while White has been trying to hold back the a-pawn, he has also had a secret agenda to achieve .... what?]

300.
[
{S:a6b7}
5 Kb7!!
Now Black must promote, or else Bxd4 wins.]

301.
[
{S:a2a1}{X:a1}{P:BQa1}
5...a1Q
Answer, checkmate!]

302.
[
{S:f6e7}
6 Be7 mate.]

303.
[
{B:kb2n3/8/1P3P2/8/K7/1N6/8/6r1}
{V:In an over-the-board game, it is often just as important to anticipate good moves for your opponent as it is to find good moves oneself. To successfully solve this study, you must firstly find Black's brilliant defense and then go on to discover the main point of the study. White to play and win.;f6f7;Correct;Incorrect.;Black has nothing better than to start checking with his rook, but it seems that White can hide his king on a6. Then Black reveals his hidden sacrificial idea, but White can reject material gain and head for mate instead.}]

304.
[
There should have been no problems with White's first move!
{S:f6f7}
1 f7]

305.
[
{S:g1g4}
1...Rg4+
If White queens his pawn, then Black faces a loss on material, but this looks like nothing more than a spite check.]

306.
[
{S:a4a5}
2 Ka5
Not 2 Ka3? Bd6+ and 3...Nf6, nor 2 Kb5? Nd6+ and 3...Nxf7.]

307.
[
{S:g4g5}
2...Rg5+]

308.
[
{S:a5a6}
3 Ka6
It is hard to see how the rook checks have helped Black, because in addition to the promotion threat White is also threatening immediate mate by b7.]

309.
[
{S:e8c7}
3...Nc7+!!
An amazing idea. Black sacrifices knight and rook in an attempt to force stalemate. The first offer has to be accepted.]

310.
[
{S:b6c7}
4 bxc7]

311.
[
{S:g5g8}
4...Rg8!
After 4...Rg6+ 5 Kb5 Rg5+ 6 Nc5 White queens in safety, so this move is forced. Now White is in a dilemma; playing fxg8Q or fxg8R delivers stalemate, but ignoring the rook completely also doesn't work, because Black is threatening ...Rf8.]

312.
[
{S:f7g8}{X:g8}{P:WBg8}
5 fxg8B!!
White matches Black's ingenuity. Normally the ending of bishop and knight against bishop is a dead draw, but in this special situation White can exploit the cornered black king.]

313.
[
{S:b8c7}
5...Bxc7]

314.
[
{S:b3d4}
6 Nd4!
The plan is Nc6, permanently imprisoning the king, and then Be6-c8-b7 mate. All the action takes place on light squares, so Black's dark-squared bishop is helpless to change the course of events. Other knight moves are ineffective, for example after 6 Nc5? Kb8 7 Be6 Bh2 Black's king escapes.]

315.
[
{S:a8b8}
6...Kb8
Black must try to flee before the knight arrives on c6, but he is mated in any case.]

316.
[
{S:d4c6}
7 Nc6+]

317.
[
{S:b8c8}
7...Kc8]

318.
[
{S:g8e6}
8 Be6 mate.]

319.
[
{B:N7/8/N7/k7/1b6/1K6/p7/6B1}
{V:White has two extra minor pieces, normally enough to win, but Black's pawn on a2 is very dangerous since 1 Kxa2? would be met by 1...Kxa6 leading to a drawn ending of bishop and knight against bishop. White to play and win.;a6c7;Correct;Incorrect.;This study is quite tricky, because White's initial attack is countered by an ingenious stalemate defense based on opposing bishops. Only precise play by White turns the tables, with stalemate being transformed into mate.}]

320.
[
{S:a6c7}
1 N6c7!
Threatening mate in one and giving Black no time to promote to a queen. Black can only avoid immediate mate by underpromoting.]

321.
[
{S:a2a1}{X:a1}{P:BNa1}
1...a1N+!
Now White cannot maintain the mating net, so he changes plan by heading for the trapped knight in the corner. An advantage of one minor piece isn't enough to win, but two minor pieces up would be too much for Black.]

322.
[
{S:b3b2}
2 Kb2]

323.
[
{S:a1b3}
2...Nb3!
Rather than just sit there waiting to be taken, the knight sacrifices itself to draw the White king into the right position for a stalemate defense.]

324.
[
{S:b2b3}
3 Kxb3
The position is the same as two moves ago, except that Black's pawn has disappeared. Surprisingly, this helps Black because he is now able to play for stalemate.]

325.
[
{S:b4c5}
3...Bc5
Not only stopping the mate on b6, but almost trapping White's bishop.]

326.
[
{S:g1h2}
4 Bh2]

327.
[
{S:c5g1}
4...Bg1
The alternative is 4...Bd6, aiming for a different perpetual attack against the bishop, but White has the reply 5 Nb6! Bxh2 (otherwise White ends up with the winning ending of bishop and knight against a lone king) 6 Nc4 mate.]

328.
[
{S:h2f4}
5 Bf4!!
White cannot use the same 5 Nb6 trick here because Black can reply with either 5...Kxb6 or 5...Bxb6. First of all the bishop must be lured onto the correct square.]

329.
[
{S:g1e3}
5...Be3
Black's bishop is like an unwelcome guest who simply won't go away, but White has found the trapdoor.]

330.
[
{S:a8b6}
6 Nb6!
Now if 6...Kxb6 (6...Bxf4 7 Nc4 mate), White reveals the point of enticing the bishop to e3, 7 Nd5+ followed by Nxe3. The only alternative is ...]

331.
[
{S:e3b6}
6...Bxb6
...but now there is no escape for Black's king.]

332.
[
{S:f4d2}
7 Bd2 mate.]

333.
[
{B:8/P7/6p1/6Pp/4R2K/8/p3B2p/6k1}
{V:This is another of those puzzles which depends only on tactics. The diagram position is already in a state of great tension. White has an extra rook and bishop, but no less than three pawns are about to promote. White to play and win.;e2f3;Correct;Incorrect.;In the main line, the first surprise is Black's second move, which gives away an apparently valuable pawn. The idea is revealed at move five, when White is unable to make the obvious capture. However, White turns the tables with his surprising sixth and seventh moves, after which Black is completely helpless.}]

334.
[
The most dangerous of the three pawns is Black's h-pawn, which threatens to promote with check. 1 a8Q? would even lose after 1...h1Q+ 2 Kg3 Qh2+ 3 Kf3 Qf2 mate. So White must take time out to cover h1, even though this allows the a1-pawn through.]

335.
[
{S:e2f3}
1 Bf3]

336.
[
{S:a2a1}{X:a1}{P:BQa1}
1...a1Q
This covers a8 but, unluckily for Black, White can promote in any case.]

337.
[
{S:a7a8}{X:a8}{P:WQa8}
2 a8Q
Apparently a very strong move, because after 2...Qxa8 3 Re1+ Kf2 4 Bxa8 Kxe1 5 Kh3 White is winning the ending, for example 5...Kf2 6 Kxh2 Ke3 7 Kg3 Kd4 8 Bc6 Ke5 9 Be8 Kf5 10 Kh4 and Black loses his pawns.]

338.
[
{S:h2h1}{X:h1}{P:BQh1}
2...h1Q+!
This finesse keeps Black in the game by setting up a stalemate possibility.]

339.
[
{S:f3h1}
3 Bxh1]

340.
[
{S:a1a8}
3...Qxa8]

341.
[
{S:e4e1}
4 Re1+]

342.
[
{S:g1h2}
4...Kh2!
Thanks to the preliminary promotion on h1, the black king has gained access to h2. Now Black threatens to take on h1, so White must act immediately.]

343.
[
{S:h1e4}
5 Be4!
Apart from acquiescing to a draw by taking on a8 this is the only move, but is a strong one, simultaneously cutting out Black's checks and setting up the threat of Rh1 mate.]

344.
[
{S:a8a1}
5...Qa1!
The only way to defend is by offering a second queen sacrifice ...]

345.
[
{S:e1b1}
6 Rb1!
... which is also declined. Curiously enough White has no threat, but Black to play can resign immediately. The only way for Black to avoid mate is to give up his queen by ...Qxb1, and this time White would definitely take it.]

346.
[
{B:n2Bqk2/5p1p/5KP1/p7/6Q1/8/8/8}
{V:White to play and win. Try to solve it on the board.;g4c8;Correct;Incorrect.;It is a shame to give any hint at all for this spectacular study, but I will reveal that White's second move is the big surprise. Black ends up with an enormous material advantage, but he is strangely helpless because of his dreadful king position.}]

347.
[
{S:g4c8}
1 Qc8!
Already an attractive move. 1 gxh7? would even lose after 1...Qxd8+ 2 Ke5 Qe7+ 3 Kd5 Qe6+ 4 Qxe6 fxe6+ 5 Kxe6 Kg7, but playing Qc8 sets up the threat of mate in two by 2 Be7+, so Black has no time to take the pawn on g6.]

348.
[
{S:f8g8}
1...Kg8
The only defense, because 1...Qe6+ 2 Qxe6 fxe6 3 gxh7 allows the pawn to slip through.]

349.
[
{S:d8c7}
2 Bc7!!
A truly incredible move. The only real alternative is 2 gxh7+ Kh8 3 Qxa8 Qe6+ 4 Kg5 Kxh7, but the ending of queen and bishop against queen is normally a draw, and here Black has two extra pawns to his credit. But why can't Black just make off with White's queen?]

350.
[
{S:e8c8}
2...Qxc8]

351.
[
{S:g6f7}
3 gxf7+]

352.
[
{S:g8h8}
3...Kh8
Forced, as 3...Kf8 allows mate in one by 4 Bd6.]

353.
[
{S:c7e5}
4 Be5
This is the position White was aiming for. He threatens mate in one by Ke7 or Kg5, and it doesn't help Black to push his h-pawn, because then White mates by Kg6 instead. Black's only defense is to attack the bishop on e5, and since his queen must retain control of f8, his reply is forced.]

354.
[
{S:c8c5}
4...Qc5
The attack on e5 has nullified the discovered checks, since 5 Ke6+, for example, is met by 5...Qxe5+ 6 Kxe5 Kg7 and Black wins easily. White must withdraw his bishop along the long diagonal in order to renew the mating threat, so the choice is between Ba1 and Bb2. Perhaps surprisingly, one move wins and the other loses. Which one is correct?]

355.
[
{S:e5b2}
5 Bb2!!
We will see later why 5 Ba1? loses. White has added the threat of Ke6 mate, Black's queen is already fully occupied dealing with the other king moves and covering f8, so he has to mobilise his last reserves.]

356.
[
{S:a8c7}
5...Nc7
An extraordinary position. Now Black cannot move his h-pawn (because of Kg6+), his knight (because of Ke6+) and his queen because of a king check or f8Q mate). Despite being a queen and a pawn up, the only thing he can move is his a-pawn.]

357.
[
{S:b2a1}
6 Ba1
White's movements are also restricted. He dare not allow Black to take the bishop with his queen, so he can only oscillate between b2 and a1.]

358.
[
{S:a5a4}
6...a4]

359.
[
{S:a1b2}
7 Bb2]

360.
[
{S:a4a3}
7...a3]

361.
[
{S:b2a1}
8 Ba1
Had White played 5 Ba1?, he would have arrived at this position with White to move. Since b2 is covered by the pawn, White would be dead lost. Black to play is forced to push his pawn, freeing b2 for the bishop.]

362.
[
{S:a3a2}
8...a2]

363.
[
{S:a1b2}
9 Bb2]

364.
[
{S:a2a1}{P:BQa1}
9...a1Q]

365.
[
{S:b2a1}
10 Bxa1
Black has run out of pass moves and must move one of his other pieces, allowing mate in at most three moves.]

366.
[
{B:2N3BK/6p1/5P1k/6p1/6PP/p7/b7/2r5}
{V:This time, white to play and draw. Try your answer on the board.;c8e7;Correct;Incorrect.;White is not only down on material, but in addition Black has a passed a-pawn which is guaranteed to carry the day if White lets up the pressure for an instant. The main thing working in White's favor is that Black's king is poorly placed. White's second and third moves are the key to the study. The second move is a surprise because White turns down an obvious capture, while
the third move is a forcing sacrifice.}]

367.
[
Once again we have a tactical free-for-all, with virtually every imaginable element being introduced during the six moves of the solution. Mate, stalemate, underpromotion, sacrifices - all play their part in creating a impression of enormous energy.]

368.
[
{S:c8e7}
1 Ne7!
A process of elimination leads to this move. The alternatives 1 Bxa2? Rxc8+ 2 Bg8 a2, 1 f7? Rxc8 and 1 hxg5+? Kxg5 2 Bxa2 Kxf6 3 Nb6 Rc2 are all hopeless, the last because Black quickly wins the bishop for the a-pawn.]

369.
[
{S:a2g8}
1...Bxg8
Black has no time for 1...gxh4 because after 2 fxg7 White's g7-pawn is decisive, while 1...gxf6? allows mate in two by 2 Nf5+ Kg6 3 h5. The capture on g8 appears very strong, because after 2 Nxg8+? Kg6 3 h5+ Kf7 4 fxg7 Rc8 5 h6 Black has an attractive win by 5...a2 6 h7 Rf8! 7 gxf8Q+ Kxf8 8 Nf6 Kf7, and next move 9...a1Q+ will force mate.]

370.
[
{S:h4h5}
2 h5!!
The solution to the dilemma is to ignore Black's bishop, and concentrate on creating threats against Black's king. This move threatens mate on f5 or g8.]

371.
[
{S:g8e6}
2...Be6
The only move, since 2...Bh7 loses to 3 fxg7 Rc8+ (or else 4 g8N+ mates) 4 Nxc8 a2 5 Nd6 followed by mate. After 2...Be6, the obvious continuation is again 3 fxg7, but then Black wins by 3...Rc8+! 4 Nxc8 a2 5 Nd6! Bxg4 (not 5...a1Q 6 Nf7+ Bxf7 stalemate) 6 Nf7+ Kxh5 7 g8Q a1Q+ 8 Qg7 (8 Kh7 Bf5+) Qa8+ 9 Qg8 Qxg8+ 10 Kxg8 Be6, followed by exchanging pieces on f7 and promoting the g-pawn. At this point it is worth stopping to work out how White proceeds.]

372.
[
{S:e7g8}
3 Ng8+!!
White is playing for stalemate, so he must get rid of the knight. White was already material down in the diagram and since then he has sacrificed both his minor pieces. Amazingly, he still manages to hold his own with the aid of his three valiant pawns.]

373.
[
{S:e6g8}
3...Bxg8]

374.
[
{S:f6f7}
4 f7
This is the idea. If Black takes the pawn then White is stalemated, but on the other hand mate in one by 5 fxg8N is threatened. 4...Bh7 loses to 5 f8Q, so Black's reply is forced.]

375.
[
{S:c1c8}
4...Rc8!
Now White's number really appears to be up. After 5 fxg8Q Rxg8+ 6 Kxg8 a2 the pawn promotes, so the only chance seems to be 5 f8Q, hoping for 5...Rxf8? with stalemate. Unfortunately, this fails after 5...Be6!, and Black wins the queen without stalemating White. It is easy to imagine that if this position arose in a game, many players
would simply resign.]

376.
[
{S:f7f8}{X:f8}{P:WBf8}
5 f8B!!
We have already seen various promotions to a knight, now here is a bishop underpromotion. The threat could not be more brutal: mate in one. Just as with a queen, 5...Rxf8 is stalemate, but unlike the queen any move by the g8-bishop is also stalemate. There is only one other move ...]

377.
[
{S:c8c7}
5...Rc7
... but stalemate is unavoidable.]

378.
[
{S:f8g7}
6 Bxg7+]

379.
[
{S:c7g7}
6...Rxg7]

380.
[
{B:2B5/pR6/2pP1k2/8/6Kb/4p1P1/5p2/8}
{V:One of the attractive features of studies is that Black often shows as much ingenuity and guile as White, much as in a first-rate over-the-board game. In this study, both sides trade tactical blows until White, with his army reduced almost to its last man, lands the last punch. White to play and win.;d6d7;Correct;Incorrect.;Black's advanced pawns are a powerful force, and White's only chance is to generate counter-play using his own d-pawn. The end result is a kind of exchange - White's d-pawn for Black's f-pawn. A side effect is that White's rook gets trapped, but while Black is rounding it up White can make the decisive bishop maneuver.}]

381.
[
Black's advanced pawns are so strong that there is little point in defending passively, for example 1 Rb1? e2 is hopeless. White's only chance is counter-attack. {S:d6d7}
1 d7]

382.
[
{S:f6e7}
1...Ke7
Forced, since after 1...f1Q 2 d8Q+ Ke5 3 Qa5+ Black has to give up his queen to avoid immediate mate.]

383.
[
{S:b7b8}
2 Rb8!
A neat tactical point. If Black plays 2...f1Q, then White wins by 3 d8Q+ Kxd8 4 Ba6+ Kc7 5 Bxf1 Kxb8 6 gxh4, followed by pushing the h-pawn.]

384.
[
{S:h4g3}
2...Bxg3!
In this study Black defends with great cunning. The obvious reply to this move is 3 Kxg3?, but then 3...f1Q 4 d8Q+ Kxd8 5 Ba6+ Kc7 6 Rb7+ Kc8 7 Rb6+ Kc7 8 Rb7+ Kc8 9 Rxa7+ Kb8 10 Rb7+ Ka8 leads to a draw, because Black can always meet Bxf1 by taking the rook, drawing because White has no pawns left.]

385.
[
{S:b8a8}
3 Ra8!
There are some tricky near-misses in this study, for example after 3 Rb4 f1Q 4 Re4+ White aims to promote with check, but Black replies 4...Be5! 5 Rxe5+ Kf6 6 d8Q+ Kxe5 bailing out to a drawn ending of queen and bishop against queen. The move 3 Ra8! threatens to blockade Black's pawns with Ba6, with a slow but sure win for White. Once again, Black finds a cunning defense.]

386.
[
{S:f2f1}{X:f1}{P:BQf1}
3...f1Q
Apparently allowing White to pick up the queen exactly as in the line given above.]

387.
[
{S:d7d8}{X:d8}{P:WQd8}
4 d8Q+]

388.
[
{S:e7d8}
4...Kxd8]

389.
[
{S:c8a6}
5 Ba6+]

390.
[
{S:g3b8}
5...Bb8!!
This is the reason why Black interpolated ...Bxg3. If White takes the bishop, the position is drawn just as after 3 Kxg3? above, for example 6 Rxb8+ Kc7 7 Rb7+ Kc8 and White cannot take the queen without losing his rook. So White has nothing better than the immediate capture of the queen, but now Black has White's rook firmly boxed in the corner.]

391.
[
{S:a6f1}
6 Bxf1]

392.
[
{S:d8c7}
6...Kc7
Intending simply ...Kb7 followed by ...Kxa8.]

393.
[
{S:f1a6}
7 Ba6
White does his best to combat Black's plan, but now the e-pawn, which has remained dormant for so long, finally emerges from hibernation to play a part in the proceedings.]

394.
[
{S:e3e2}
7...e2!]

395.
[
{S:a6e2}
8 Bxe2]

396.
[
{S:c7b7}
8...Kb7
One cannot help but feel sorry for Black, who has fought with tremendous resourcefulness, but fails just when he is on the threshold of forcing a draw.]

397.
[
{S:e2f3}
9 Bf3
Threatening 10 Bxc6+, so Black has no way out.]

398.
[
{S:b7a8}
9...Kxa8]

399.
[
{S:f3c6}
10 Bxc6 mate.]

400.
[
{B:8/8/6Q1/q7/k1n5/8/4P3/K2R1Nn1}
{V:It may seem odd to talk about visual effects in chess, but the whole basis of the game is geometrical and composers often strive to emphasize the element of visual paradox inherent in chess. The final position of this study is an excellent example of a purely optical effect. White to play and draw.;d1d2;Correct;That is incorrect.;Even White's first move is quite tough, but you should bear in mind a common method of defending against a kingside attack in over-the-board play, namely playing a rook to the second rank. In the later play Black appears to be making all the running, but White comes up with an incredible last-ditch defense.}]

401.
[
White's situation in the diagram appears to be utterly desperate. There are threats of mate by ...Qc3+, ...Qe5+ and ...Kb3+, and any kind of defense is hard to come by, for example 1 Kb1? Qb4+ 2 Kc2 Qb2+ 3 Kd3 Ne5+, 1 Ka2? Kb5+! 2 Kb1 Qb4+, 1 Qd3? Kb5+!, 1 Qc2+? Kb4+ 2 Kb1 Na3+ or 1 Rd3? Qe5+. The most tempting try is 1 Qg3?, but this loses to 1...Nxe2! 2 Qb8 Qc3+ 3 Ka2 (3 Kb1 Na3+ 4 Ka2 Qc2+) Qc2+ 4 Ka1 Qxd1+ 5 Qb1 Qd4+ and Black mates.]

402.
[
{S:d1d2}
1 Rd2!
Absolutely the only move. White would be quite happy for Black to take the rook, since 1...Nxd2 2 Nxd2 would be an easy draw, but of course Black continues the attack.]

403.
[
{S:a4b3}
1...Kb3+
Other possibilities aren't dangerous, for example 1...Qc3+ 2 Ka2 Qb3+ 3 Ka1, 1...Kb4+ 2 Ra2 Qe5+ 3 Kb1 or 1...Kb5+ 2 Kb1 Qb4+ 3 Kc1 Qc3+ 4 Kb1.]

404.
[
{S:a1b1}
2 Kb1]

405.
[
{S:c4a3}
2...Na3+]

406.
[
{S:b1c1}
3 Kc1
Certainly not 3 Ka1? Nc2+ and mate next move.]

407.
[
{S:a5c3}
3...Qc3+
After 3...Qc5+ or 3...Qc7+ White can simply run away with his king by 4 Kd1, but now 4 Kd1 would be met by 4...Qa1 mate. 4 Rc2 is met by 4...Qe1 mate, so it is hard to see what White can do apart from resign.]

408.
[
{S:g6c2}
4 Qc2+!!
Up to this point White has been desperately fending off Black's threats, but with this unusual sacrifice White takes the driver's seat, albeit at a heavy material cost.]

409.
[
{S:a3c2}
4...Nxc2]

410.
[
{S:d2d3}
5 Rd3
The consequence of White's previous move, but what about the apparently devastating response ...]

411.
[
{S:g1e2}
5...Nxe2+]

412.
[
{S:c1d1}
6 Kd1!]

413.
[
{S:c3d3}
6...Qxd3+]

414.
[
{S:f1d2}
7 Nd2+
An amazing position. Black has an extra queen and knight, but thanks to the oddly symmetrical grouping of his pieces he has taken away the only squares from the white king. Black has the choice between moving his king, with stalemate, or playing ...Qxd2+, when the drawn ending of king and two knights against king arises.]

415.
[
{B:8/7p/6Nk/5p1P/7P/1p3K2/6p/6B1}
{V:White to play and win.;g1e3;Correct;Incorrect.;White has trouble coping with Black's two advanced pawns, so he has to combine maneuvers against the pawns with threats against the Black king. Accuracy is required, however, since 1 Nf4? b2 2 Bc5 is met by 2...g1Q! 3 Bxg1 Qxb1, and Black promotes safely.}]

416.
[
{S:g1e3}
1 Be3+!
Not 1 Nf4? b2 2 Bc5 g1Q! 3 Bxg1 b1Q, nor 1 Bd4? hxg6.]

417.
[
{S:f5f4}
1...f4! 
The best defense, since 1...Kg7 (1...Kxh5 2 Nf4+, followed by 3 Nxg2+ and 4 Bc1, stops the pawns and wins for White) 2 Kxg2 hxg6 3 h6+ Kh7 4 Bc1 f4 (otherwise White just advances his king to g5) 5 Kf3 Kxh6 6 Kg4! is winning, for example 6...Kg7 7 Kxf4 or 6...b2 7 Bxb2 f3 8 Bd4.]

418.
[
{S:g6f4}
2 Nxf4
Black's idea was that 2 Bxf4+ could be met by 2...Kxh5, and now the square f4 is not available for the knight.]

419.
[
{S:g2g1}{D:100}{X:g1}{P:BQg1}
2...g1Q!
Black cannot play 2...b2 immediately, because of 3 Nd3+ and 4 Nxb2, so first he must deflect White's bishop.]

420.
[
{S:e3g1}
3 Bxg1]

421.
[
{S:b3b2}
3...b2
This is the critical moment. Black's counter-play has become serious, but his king is caught in a trap. If you have not already worked out the rest of the study, stop here and try to figure it out. White's most obvious move meets with a cunning defense, but of course White has the last laugh.]

422.
[
{S:g1c5}
4 Bc5
What else? White can no longer stop the pawn, so he has to play for mate.]

423.
[
{S:h6g7}
4...Kg7
The only move to prevent mate, but what about the simple reply 5 Bd4+?]

424.
[
{S:c5d4}
5 Bd4+]

425.
[
{S:g7h6}
5...Kh6!
This is the whole point of Black's defense. Taking the pawn is stalemate, while playing 6 Bc5 is just a draw by repetition. In order to win White has to abandon the mating net with Black's king on h6 and substitute a new one with the king on h4, something which is hard to see for psychological reasons.]

426.
[
{S:f4e6}
6 Ne6!
Now the pawn is threatened, so Black must promote.]

427.
[
{S:b2b1}{D:100}{X:b1}{P:BQb1}
6...b1Q
Black is ahead on material, but White can hunt the enemy king to its doom.]

428.
[
{S:d4g7}{D:1000}{S:h6h5}
7 Bg7+
7...Kxh5]

429.
[
{S:e6f4}
8 Nf4+]

430.
[
{S:h5h4}
8...Kxh4]

431.
[
{S:g7f6}
9 Bf6 mate.]

432.
[
{B:5r2/8/1R6/ppk3p1/2N3P1/P4b2/1K6/5B2}
{V:White has an extra piece, but his knight and rook are under threat, so he faces the immediate loss of his extra material. White to play and win.;b6b5;Correct;Incorrect.;The solution starts with a mini-combination, which either saves White's extra piece or forces Black's king into a horribly dangerous position. It seems that mate in a couple of moves is inevitable, but Black finds a remarkable stalemate defense, which is only refuted by a totally outrageous idea. 1 Ne5? Kxb6 2 Nd7+ Kc6 3 Nxf8 Bxg4 and now White cannot avoid the exchange of his last pawn, for example after 4 Nh7 Bd1 5 Nxg5 b4, and Black reaches the sanctuary of a drawn ending with bishop and knight against bishop.}]

433.
[
{S:b6b5}
1 Rxb5+!
The first of many sacrifices by both players. Black's king is deflected onto a square allowing a discovered check.]

434.
[
{S:c5b5}
1...Kxb5]

435.
[
{S:c4e5}
2 Ne5+]

436.
[
{S:b5a4}
2...Ka4
This is obviously a dangerous spot for the king, but there is no choice because the other two legal king moves both allow Nd7+ capturing the rook. This is winning because Black has lost his b-pawn, so there is no chance that he can exchange off White's last pawn.]

437.
[
{S:e5d7}
3 Nd7
The obvious move. White attacks the rook, stops the check on b8 and threatens two different mates in one. It is worth pausing here to find the subtle defense which Black now plays.]

438.
[
{S:f3e2}
3...Be2!!
Black is aiming for stalemate, so first of all he must jettison his bishop. Sacrificing the pieces in the other order is no good, since after 3...Rb8+ 4 Nxb8 Be2 White can simply play 5 Bg2.]

439.
[
{S:f1e2}
4 Bxe2
White cannot refuse the sacrifice by 4 Bg2, because after 4...Rf2! 5 Bc6+ Bb5+ White is in check, and so has no time for a knight mate.]

440.
[
{S:f8b8}
4...Rb8+
If White takes the rook it is stalemate, so there appears to be nothing better than 5 Kc3 (5 Ka2 Rb2+! also draws) Rb3+ 6 Kd4 Kxa3, but then Black's dangerous passed a-pawn guarantees a comfortable draw. The move which actually wins is one of the most remarkable I have ever seen.]

441.
[
{S:e2b5}
5 Bb5+!!
After 5...Kxb5 the stalemate is gone and White can safely take the rook, so Black's reply is forced.]

442.
[
{S:b8b5}
5...Rxb5+]

443.
[
{S:b2a2}
6 Ka2
Black has to move his rook, but incredibly the rook is trapped. It can only avoid immediate capture by moving to b3, b7 or d5, but in every case White wins it with a knight fork. The result is that White emerges with a clear extra piece, leading to an easy win.]

444.
[
{B:8/4P3/8/4br1B/2R3p1/8/6p1/2K1k3}
{V:In this study it is important to bear in mind that the ending of rook and bishop against rook is generally a draw. White to play and win.;c1b1;Correct;Incorrect.;The solution is only seven moves long, but the tactics are fairly complex. There are various lines in which both sides promote, and the big question is whether or not White can win. In most cases he cannot, but in the main line White succeeds in reaching a situation where he can indeed win, and in the most spectacular manner imaginable. White's tricky first move introduces all the tactics, and is based on the idea of preventing ...g1Q by threatening a rook check on the first rank. 1 Re4+? Kf2 2 Rxg4 Bg3 is better for Black. 1 Rxg4? Bf4+ 2 Rxf4 Re5 3 Rg4 Kf2 is a draw.}]

445.
[
{S:c1b1}
1 Kb1!
Already quite a tough move to find. The immediate 1 e8Q? g1Q is bad for White because the only check, 2 Re4+, is itself met by a check, 2...Kf2+, and Black gains the initiative. A more reasonable try is 1 Rxg4?, but after 1...Bf4+ 2 Rxf4 (or else ...Re5 in any case) Re5 3 Rg4 Kf2 Black secures an easy draw. Finally, 1 Re4+? Kf2 2 Rxg4 is met by 2...Bg3 and Black threatens to promote with check.]

446.
[
{S:f5f1}
1...Rf1!
Black cannot promote, because first of all he must deal with the possibility of Rc1+. After 1...Kf2 White plays 2 Rc2+ and 3 Rxg2, after which he can safely promote the e-pawn.]

447.
[
{S:c4g4}
2 Rxg4
Curiously, although the two pawns stand ready to promote, both players have more important matters to attend to first. The immediate 2 e8Q? (2 Rc1+? Kd2 even loses for White) is bad because of 2...Kd2+ 3 Ka2 Ra1+ 4 Kb3 Rb1+ 5 Ka4 g1Q, and although White has the first check, he cannot force mate because Black's pieces are too active, for example 6 Qd7+ Ke3 7 Qa7+ Kf3 and Black is safe.]

448.
[
{S:e5g3}
2...Bg3!
The best defense. It is tempting to play 2...Kf2+ 3 Kc2 Bg3, but after 4 Re4! Black cannot promote because of mate on e2, while otherwise Re2+ will eliminate the g-pawn, and then White's own pawn will decide the game.]

449.
[
{S:e7e8}{D:100}{X:e8}{P:WQe8}
3 e8Q+
At last the moment comes for White to promote his pawn. 3 Rxg3? is bad because of 3...Kf2+ and 4...Kxg3, while after 3 Kc2? Rf2+ 4 Kd3 Re2 Black stops the White pawn, leading to the drawn ending of rook and bishop against rook after 5 Rxg3 Rxe7 6 Rxg2.]

450.
[
{S:e1f2}
3...Kf2+
The best square for the king, since 3...Kd2+ 4 Kb2 g1Q allows mate in five by 5 Qd8+ Ke3 6 Qd4+ Kf3 7 Qd5+ Ke2 8 Re4+ Kf2 9 Qd2 mate.]

451.
[
{S:b1c2}
4 Kc2
We shall see in a moment why this move wins, and no other.]

452.
[
{S:g2g1}{D:100}{X:g1}{P:BQg1}
4...g1Q
Another position with two queens. A move such as 5 Qf7+ leads to nothing after 5...Kg2, because Black's pieces are well placed to defend the king.]

453.
[
{S:e8e2}
5 Qe2+!!
This queen sacrifice is the only winning move. Suddenly, the clustering of Black's pieces, normally so helpful in defense, turns out to be a fatal handicap.]

454.
[
{S:f2e2}
5...Kxe2]

455.
[
{S:g4e4}
6 Re4+
Now we can see why White's king had to move to c2.]

456.
[
{S:e2f2}
6...Kf2]

457.
[
{S:e4e2}
7 Re2 mate.]

458.
[
{B:8/6KP/6P1/8/3k4/8/p6B/b7}
{V:There is no question that this is hardest of the endgame studies. Although the position appears relatively simple, extremely subtle play is required by both players. However, all the analytical effort is worthwhile when one finds the remarkable conclusion to the study. White to play and draw.;g7g8;Correct;Incorrect.;Various endings can arise in the course of the solution, which need to be accurately evaluated. Here are some useful guidelines, firstly, an ending with a black queen against White's bishop and h7-pawn is winning for Black if his king is close enough to the h8-corner, for example if his king is on e6 or f5. Secondly, a similar ending is drawn if White still has his g6-pawn. An ending with queen against bishop and g7-pawn is lost for White.}]

459.
[
{S:g7g8}
1 Kg8
The immediate promotion is no good, because Black wins after 1 h8Q? Ke4+ 2 Kg8 Bxh8 3 Kxh8 a1Q+ 4 g7 Kf5 5 Kh7 Qa7 6 Kh8 Qd4 7 Kh7 Qh4+ 8 Kg8 Kg6, forcing a quick mate. Likewise, 1 Bg3? Ke4+ 2 Kg8 Kf5 3 g7 Bxg7 4 Kxg7 a1Q+ is an easy win for Black. Endings with a black queen against bishop and pawn(s) arise quite often in this study. The general rule is that if White still has both kingside pawns then he can draw, but if he has only one pawn left then he loses.]

460.
[
{S:d4e4}
1...Ke4
It is hard to see why this is better than moving to d5, but after 1...Kd5 2 Bf4! White draws more comfortably. The basic idea is that after a move such as 2...Bb2, White opposes bishops by 3 Bc1; then 3...a1Q 4 Bxb2 Qa8+ 5 Kg7 is a comfortable draw, while 3...Bc3, for example, is answered by 4 Bd2 with the same situation. If Black plays 2...Bh8, then 3 Kxh8 a1Q+ 4 Kg8 is the same. Finally, 2...Ke6 is met by 3 Bh6! Bc3 (3...Kf5 4 g7 and 3...Bh8 4 Kxh8 a1Q+ 5 Kg8 are also drawn) 4 h8Q! Bxh8 5 g7, forcing a draw.]

461.
[
{S:h2d6}
2 Bd6!
There is a large element of symmetry in the position, so it is not surprising that if 2...Kd5 is met by 3 Bf4!, then 2...Ke4 should be met by 3 Bd6!.]

462.
[
{S:e4f5}
2...Kf5
If Black plays 2...Bb2, then White draws much as above, for example 3 Ba3 a1Q 4 Bxb2 Qa8+ 5 Kg7 Qb7+ 6 Kg8 (but not 6 Kh6? Qxb2 7 g7 Qf6+ winning the pawns) Qb8+ 7 Kf7 Qxb2 8 g7 and the two connected passed pawns are too strong for Black to win. However, the move played explains why 1...Ke4 was better than 1...Kd5; in the note to Black's first move, 1...Kd5 2 Bf4! Ke6 3 Bh6 Bh8 4 Kxh8 a1Q 5 Kg8 was a fairly comfortable draw. However, the symmetrical line is winning for Black.]

463.
[
{S:d6f8}
3 Bf8!
Initially White plays the same way, relying on the stalemate defense 3...Kxg6 4 h8Q! Bxh8 5 Bg7 Bxg7. However, Black has a surprising finesse.]

464.
[
{S:a1h8}
3...Bh8!!
Now White appears to be in trouble, because Black's king is already attacking g6, so 4 Kxh8 loses to 4...a1Q+ 5 Kg8 Qa2+ 6 Kg7 Qa7+ 7 Kg8 (7 Kh6 Qe3+ 8 Kg7 Qe5+ wins after 9 Kh6 Qf6 or 9 Kg8 Qe6+) Kxg6 8 h8N+ Kf6 9 Bh6 Qe7 10 Bf8 Qe8 and White has no moves.]

465.
[
{S:g6g7}
4 g7!
This is the only real alternative.]

466.
[
{S:a2a1}{D:100}{X:a1}{P:BQa1}
4...a1Q
What now? After 5 gxh8Q, Black forces mate by 5...Qa2+ 6 Kg7 Qb2+ 7 Kg8 Qb3+ 8 Kg7 Qc3+ 9 Kg8 Qc4+ 10 Kg7 Qd4+ 11 Kg8 Qd5+ 12 Kg7 Qe5+ 13 Kg8 Qe6+ 14 Kg7 Qg6 mate. The other obvious possibility is 5 Kxh8?, but 5...Kg6 6 Kg8 Qd4 7 h8N+ (7 Kh8 Kf7) Kf6 8 Kh7 (8 Nf7 Qd5 9 Kh8 Qh5+) Qh4+ 9 Kg8 Qh5 is winning for Black. Only the bishop can move, but wherever it goes, Black can always pick it up with queen checks, for example 10 Ba3 Qd5+ 11 Kh7 Qd3+ 12 Kg8 Qxa3, with mate in a few more moves. Have a look at the position for a few moments to work out how White defends himself.]

467.
[
{S:g7h8}{D:100}{X:h8}{P:WNh8}
5 gxh8N!
The only move, allowing White to interpose after a check on a2. With a bishop, knight and advanced pawn for the queen White has plenty of material to draw, but his king is still in an awkward spot.]

468.
[
{S:a1a2}
5...Qa2+]

469.
[
{S:h8f7}
6 Nf7!
Not 6 Kg7? Qe6 7 Ba3 (7 Nf7 Qg6+ also wins) Qe5+ 8 Kg8 Kf6 and White cannot avoid mate.]

470.
[
{S:f5g6}
6...Kg6
Black's last throw.]

471.
[
{S:h7h8}{D:100}{X:h8}{P:WNh8}
7 h8N+!
Now the cluster of minor pieces round the king provides an adequate defense, and White draws easily. Looking at the initial position, it is hard to imagine that the only way to draw is for White to promote both his pawns to a knight.]

472.
[
{F:B}{B:24/N7/16/5p2/k1K5 BLACK}
{V:The final seven puzzles explore the wilder fringes of puzzledom. This puzzle is a serieshelpmate in 17, which means that Black plays seventeen consecutive moves, without White moving at all, to reach a position in which White can mate in one. Just as in a normal helpmate, both sides are cooperating. There is one additional rule, none of Black's moves are allowed to give check, except possibly on the last move of the series. Serieshelpmate in 17.;a1a2;Correct;Incorrect.;If a2 were blocked, then White could mate in one by Nb3. The blocking piece must be a rook (if it were a knight, White would be in check and would have no time for the knight mate). Clearly, the f2-pawn must promote to a rook and then move to a2, but at the moment this is not allowed because it would give check.}]

473.
[
The only possible mating position is with a black rook on a2, allowing mate by Nb3. A black knight is no good, because White would be in check and would have no time for Nb3. Black cannot promote his pawn to a rook directly because this would deliver check. So first of all Black must use his king as a shield to block the first rank so that he can promote his pawn, and he must not waste time so he must use the shortest route from a1 to e1.]

474.
[
{S:a1a2}
1...Ka2]

475.
[
{S:a2a3}
2...Ka3]

476.
[
{S:a3b4}
3...Kb4]

477.
[
{S:b4c3}
4...Kc3]

478.
[
{S:c3d3}
5...Kd3]

479.
[
{S:d3e2}
6...Ke2]

480.
[
{S:e2e1}
7...Ke1
Now the pawn can promote.]

481.
[
{F:B}{B:24/N7/16/5p2/2K1k3}
{S:f2f1}{D:100}{X:f1}{P:BRf1}
8...f1R
Black's king must return to a1, but first the rook must move or else ...Ke2 will be check.]

482.
[
{S:f1f2}
9...Rf2
The rook must not move to a2 prematurely, because then the black king's return path will be blocked.]

483.
[
{S:e1e2}
10...Ke2]

484.
[
{S:e2d3}
11...Kd3]

485.
[
{S:d3c3}
12...Kc3]

486.
[
{S:c3b4}
13...Kb4]

487.
[
{S:b4a3}
14...Ka3]

488.
[
{S:a3a2}
15...Ka2]

489.
[
{S:a2a1}
16...Ka1
Everything is in place, and the mating position can be set up.]

490.
[
{S:f2a2}
17...Ra2]

491.
[
{S:a5b3}
18 Nb3 mate.
It is interesting to note how the composer ensured that the order of Black's moves was absolutely unique.]

492.
[
{F:B}{B:K2k4/1pN5/3p1p1p/3P1P1P/7P/8/4P3/8 BLACK}
{V:Despite their length, serieshelpmates are usually quite easy to solve. The technique is the same as for helpmates, first the mating position must be identified and then the method of reaching it determined. Serieshelpmates lend themselves to unusual effects involving pawn promotion. This is one example. Serieshelpmate in 30.;b7b5;Correct;Incorrect.;It is a fairly obvious guess that White will mate by Ne6 after the squares c8, d7, e7 and e8 have been blocked. This means that all the black pawns will promote during the solution. The only problem is to work out which pawn promotes to which piece.}]

493.
[
White will mate by Ne6 after Black's four pawns have promoted and occupied the squares c8, d7, e7 and e8. At present only one Black pawn can move, so the first four moves are easy.]

494.
[
{S:b7b5}
1...b5]

495.
[
{S:b5b4}
2...b4]

496.
[
{S:b4b3}
3...b3]

497.
[
{S:b3b2}
4...b2]

498.
[
{F:B}{B:K2k4/2N5/3p1p1p/3P1P1P/7P/8/1p2P3/8}
Now Black faces the first promotion decision. After the pawn promotes, it will have to free another pawn as it moves towards its final destination. The obvious pawn to take is the one on f5, but should Black promote to a bishop or a queen? If Black takes a queen, and then plays ...Qxf5, then he cannot move to c8 (as this would be check) and it is no good blocking d7, because then Ne6 won't be mate. This suggests that a bishop is the correct choice.]

499.
[
{S:b2b1}{D:100}{X:b1}{P:BBb1}
5...b1B]

500.
[
{F:B}{B:K2k4/2N5/3p1p1p/3P1P1P/7P/8/4P3/1B6}
{S:b1f5}
6...Bxf5
The bishop should not move to d7, as this would prevent the final mate.]

501.
[
{S:f5c8}
7...Bc8]

502.
[
{S:f6f5}
8...f5]

503.
[
{S:f5f4}
9...f4]

504.
[
{S:f4f3}
10...f3
Now Black has to choose whether to promote on e1 or on f1. The answer comes from considering which type of piece will capture White's pawn on d5 to release the d6-pawn. It cannot be a bishop or queen, because this would give check, so it must be a rook or a knight. A rook appears possible, since afterwards it could move to e5 and e8, but this appears unlikely because after ...Rxd5 and ...Re5, there is no visible reason why Black should not play either ...d5 or ...Re8 next (the order of Black moves is always unique in a serieshelpmate). This suggests that a knight takes on d5, which is plausible because it could move to its final destination (e7) in only one move.]

505.
[
{S:f3f2}
11...f2]

506.
[
{F:B}{B:K1bk4/2N5/3p3p/3P1P1P/7P/8/4Pp2/8}
{S:f2f1}{D:100}{X:f1}{P:BNf1}
12...f1N]

507.
[
{S:f1e3}
13...Ne3]

508.
[
{S:e3d5}
14...Nxd5]

509.
[
{S:d5e7}
15...Ne7]

510.
[
{S:d6d5}
16...d5]

511.
[
{S:d5d4}
17...d4]

512.
[
{S:d4d3}
18...d3
Again, Black has a choice of promotion square, but now it is easier. By promoting to a queen on e1, Black can remove the pawns on h4 and h5 without loss of time, and then head for e8.]

513.
[
{S:d3e2}
19...dxe2]

514.
[
{F:B}{B:K1bk4/2N1n3/7p/7P/7P/8/4p3/8}
{S:e2e1}{D:100}{X:e1}{P:BQe1}
20...e1Q]

515.
[
{S:e1h4}
21...Qxh4]

516.
[
{S:h4h5}
22...Qxh5]

517.
[
{S:h5e8}
23...Qe8
Now the last pawn heads for the first rank.]

518.
[
{S:h6h5}
24...h5]

519.
[
{S:h5h4}
25...h4]

520.
[
{S:h4h3}
26...h3]

521.
[
{S:h3h2}
27...h2]

522.
[
{F:B}{B:K1bkq3/2N1n3/32/7p/8}
{S:h2h1}{D:100}{X:h1}{P:BRh1}
28...h1R]

523.
[
{S:h1d1}
29...Rd1
Finally...]

524.
[
{S:d1d7}
30...Rd7]

525.
[
{S:c7e6}
31 Ne6 mate.
The curious feature of this problem is that each of the four black pawns had to promote to a different piece.]

526.
[
{F:W}{B:1n2k3/ppp1n2p/4p3/6pq/2r5/2b2p1b/PPPPPPPP/RNBQKBNR WHITE}
Here is yet another type of puzzle - a reconstruction problem. These depend as much on logic as skill at chess, but for that reason they offer a welcome change from the endless 'Find the Combinations' puzzles so beloved of chess magazines. This is the position after Black's 14th move, what was the game?]

527.
[
The first step is to count the number of moves required for Black's pieces to arrive in their diagram positions. Then it will be possible to determine the fate of the two missing black pieces. The next stage is to determine when the pawn on d7 was captured, and when the rook on a8 disappeared. A final leap of the imagination will be necessary for the complete solution.]

528.
[
Black's bishops have made at least three moves, his pawns five, his queen two, his c4-rook three and his knight one - total 14. Thus neither the b8-knight nor the d7-pawn ever moved, and both must have been captured on their original squares by white knights. It follows that the rook on c4 started life on h8.]

529.
[
{B:rnbqkbnr/pppppppp/32/PPPPPPPP/RNBQKBNR}
Now we have to work out the order of Black's moves. Which moves can Black play before the d7-pawn is captured? Note that ...e6 must come after ...Bh3, and ...Ne7 must follow ...e6. This releases the h8-rook to move to c4. Therefore the Ng8, Rh8 and Pe7 cannot move until after White plays Nxd7. Black's queen must have reached h5 via d5, g5 or h4, so Black cannot play ...g5 until after at least one queen move, or else the queen cannot reach h5 in two moves. Thus the Pg7 and hence also the Bf8 cannot move until after Nxd7. In other words, the only moves Black can make before the d7-pawn is captured are ...f5, ...f4 and ...f3. Then Black runs out of moves, so White must play Nxd7 by move three. This determines the first few moves.]

530.
[
{S:g1f3}
1 Nf3]

531.
[
{S:f7f5}
1...f5]

532.
[
{S:f3e5}
2 Ne5]

533.
[
{S:f5f4}
2...f4]

534.
[
{S:e5d7}
3 Nxd7]

535.
[
{S:f4f3}
3...f3
Now we have to work out how the a8-rook is taken. In the final position White has a knight on g1, and since f3 is now blocked it must arrive there via h3. The obvious plan is 4 Nb6 5 Nxa8 6 Nb6 7 Nd5 8 Nf4 and 9 Nh3, but in fact this is impossible. The reason is that with this sequence Black cannot play ...Bh3 until move 10 at the earliest, but at least five moves (...e6, ...Ne7 and three with the rook) must follow ...Bh3, and there is no time for these. It follows that it is the knight on b1 which heads for h3. So White must continue 4 Nb6 (the d7-knight must move, because Black has no more pass moves) and then play the Nb1 to g1 (via h3), which takes us up to move nine (Black's ninth move must be ...Bh3), finally 10 Nxa8 and back to b1 consumes all the white moves.]

536.
[
{S:d7b6}
4 Nb6
Black's last six moves are 9...Bh3, 10...e6, 11...Ne7 and rook to c4. Since the pawn stays on e7 until move 10, the black queen must reach h5 via d5. This must occur before ...g5, which releases the f8-bishop for ...Bg7-c3. Now we have completely determined the order of Black's moves.]

537.
[
{S:d8d5}
4...Qd5]

538.
[
{S:b1c3}
5 Nc3]

539.
[
{S:d5h5}
5...Qh5]

540.
[
{S:c3d5}
6 Ncd5
Not 6 Ne4?, intending Ng5-h3, because Black's next move must be ...g5.]

541.
[
{S:g7g5}
6...g5]

542.
[
{S:d5f4}
7 Nf4]

543.
[
{S:f8g7}
7...Bg7]

544.
[
{S:f4h3}
8 Nh3]

545.
[
{S:g7c3}
8...Bc3]

546.
[
{S:h3g1}
9 Ng1]

547.
[
{S:c8h3}
9...Bh3]

548.
[
{S:b6a8}
10 Nxa8]

549.
[
{S:e7e6}
10...e6]

550.
[
{S:a8b6}
11 Nb6]

551.
[
{S:g8e7}
11...Ne7]

552.
[
{S:b6c4}
12 Nc4]

553.
[
{S:h8f8}
12...Rf8]

554.
[
{S:c4a3}
13 Na3]

555.
[
{S:f8f4}
13...Rf4]

556.
[
{S:a3b1}
14 Nb1]

557.
[
{S:f4c4}
14...Rc4
Voila!
Looking at the diagram position, it is not obvious that White's knights must have changed places.]

558.
[
{B:rnbqkbnr/pppppppp/32/PPPPPPPP/RNBQKBNR}
A game starts 1 e4 and ends on move five when a knight takes a rook, delivering mate. What is the game? Every puzzle collection should have one really tough problem, and here it is! I remember GM Mestel showing this puzzle in the hotel lobby during the 1976 Haifa Olympiad. Soon there was a group of more than a dozen leading players clustered silently around a chessboard on which the move 1 e4 had been played. One of hotel staff came up to see what had attracted such a crowd, but when he saw what they were doing, he went away shaking his head in disbelief at these crazy chess players.]

559.
[
Anybody who solves this puzzle in less than 24 hours (without looking at the hint-coming up next) is doing very well indeed.]

560.
[
Hint- First of all, we have to decide who delivers the mate. If White mates, then there is half a move less to play with, and in addition White is committed to 1 e4. It turns out that the four remaining moves are insufficient to arrange a mate, so it is Black who plays the mating move. The (fairly large) hint is that Black cannot deliver the mate using only the knight. It is necessary for another piece to be brought into the game.]

561.
[
There is not really any logical way of deducing the solution, which of course is why it is so hard. You just have to try various ideas until one of them works. Perhaps the key idea is that the problem is impossible so long as Black relies only on the knight. Another piece has to enter the game. The solution runs...]

562.
[
{S:e2e4}
1 e4]

563.
[
{S:g8f6}
1...Nf6]

564.
[
{S:f2f3}
2 f3]

565.
[
{S:f6e4}
2...Nxe4]

566.
[
{S:d1e2}
3 Qe2
White's first three moves can be played in a slightly different order.]

567.
[
{S:e4g3}
3...Ng3]

568.
[
{S:e2e7}
4 Qxe7+]

569.
[
{S:d8e7}
4...Qxe7+]

570.
[
{S:e1f2}
5 Kf2]

571.
[
{S:g3h1}
5...Nxh1 mate.]

572.
[
{B:rnbqkbnr/pppppppp/32/PPPPPPPP/RNBQKBNR}
A game ends on move five when one player mates by underpromoting to knight. What is the game? This bears a superficial similarity to the previous puzzle, but it is much simpler.]

573.
[
Hint- There is no reason not to take the extra half-move offered by having Black deliver the mate. All Black's moves are pawn moves but, just as in the preceding puzzle, the important point is that another Black piece has to play a part in the final mate.]

574.
[
It is clearly going to help if Black delivers the mate, because then there is an extra half-move. Just as in the previous puzzle, there is no chain of logic leading to the solution, you simply have to keep trying.]

575.
[
There are some interesting near-misses, for example 1 f3 2 h3 3 Kf2 4 Kg3 and 5 Kh2 fails only because White's queen can take the promoting pawn on f1. The key idea is to get another Black piece to play a part in the mating position. The solution runs...]

576.
[
{S:d2d3}
1 d3]

577.
[
{S:e7e5}
1...e5]

578.
[
{S:b2b3}
2 b3]

579.
[
{S:e5e4}
2...e4]

580.
[
{S:e1d2}
3 Kd2]

581.
[
{S:e4d3}
3...exd3]

582.
[
{S:d2c3}
4 Kc3]

583.
[
{S:d3e2}
4...dxe2
White can vary the order of his first four moves, and it is also possible or White to play d4 instead of d3.]

584.
[
{S:c3b2}
5 Kb2]

585.
[
{S:e2d1}{D:100}{X:d1}{P:BNd1}
5...exd1N mate.]

586.
[
{B:24/1r1b4/B7/16/3k4}
{I:White's king has been knocked off the board. Where was it? Click the square it was on, then click Done. Hint - At some point you will probably conclude that the position is impossible and that there is no square for White's king which results in a legal position. At this moment you will be very close to finding the answer.;c3;Correct.;That's not the correct square.}]

587.
[
If White were to play, then his king would have to be on b3 or Black would be in check, but then White's own king would be in an impossible double check.]

588.
[
Therefore Black is to play. What has White just played?]

589.
[
It could not have been a bishop move, so it must have been a king move. Black could not have been in check before White's last move, so White has just moved his king from b3, possibly capturing something in the process. It follows that White's king was in double check from rook and bishop before his last move. We have almost argued ourselves into a corner because this double check appears impossible. The difference is that now there can be another black unit on the board, which is about to be captured by White's king.]

590.
[
Now we are almost at the end. The only unit which could possibly make a difference is a black pawn, which could be on c3 as a result of the sequence c2-c4 b4xc3+. White then plays Kb3xc3, reaching the diagram position.]

591.
[
This puzzle is based on the fact that the only way you can give a double check without moving one of the checking pieces is by means of an en passant capture.]

592.
[
{B:24/1r1b4/B7/2K5/8/3k4}
Therefore White's king stands on c3.]

593.
[
{B:6BB/6pR/6k1/4K1p1/32 BLACK}
{V:White mates in four.
At first there doesn't appear to be anything at all unusual about this problem, but ...;g5g4;Correct;Incorrect.;Any hint would give the solution away completely, so just for once I am keeping quiet!}]

594.
[
There is a small trick involved in the problem (I am allowed this once in 50 puzzles).]

595.
[
Doubtless many of you thought that the solution was 1 Bxg7 g4 2 Kf4 g3 3 Bf8, followed by 4 Rh6 mate, but alert readers will have noticed that the condition is 'White mates in four' and not 'White to play and mate in four'.]

596.
[
Suppose that White is to play in the diagram. Then Black's last move was either a king move, or a pawn capture h6xg5. If the king has just moved, it must have come from f7, h5 or h6, but in every case there is no way that the white checking piece could have arrived on its present square. On the other hand, if ...h6xg5 was the previous move then the bishop on h8, which must be a promoted pawn, could only have arisen as a result of g6xh7 and h7-h8B. But then there would be a white bishop on h8, and black pawns on g7 and h6, so there would be no way for a white rook to reach h7.]

597.
[
It follows that the diagram position is impossible if White is to play. Therefore, Black is to move and the solution is...]

598.
[
{S:g5g4}
1...g4]

599.
[
{S:h7g7}
2 Rxg7+]

600.
[
{S:g6h5}
2...Kh5]

601.
[
{S:e5f4}
3 Kf4]

602.
[
{S:g4g3}
3...g3]

603.
[
{S:f4f5}
4 Kf5]

604.
[
{S:h5h4}
4...Kh4]

605.
[
{S:g7h7}
5 Rh7 mate.]