40th World Chess Solving Championship – solutions

[Event "Mate in two"] [Site "?"] [Date "1969.??.??"] [Round "?"] [White "Schonholzer, Andreas"] [Black "3rd Przie, Freie Presse"] [Result "*"] [Annotator "John Nunn"] [SetUp "1"] [FEN "8/b2q1nN1/5P2/2nQ2pN/6k1/5pB1/3rp2R/3bR2K w - - 0 1"] [PlyCount "3"] [EventDate "1969.??.??"] {The white queen is under attack from two black pieces, so White must make a fairly brutal threat to have a chance of mating in two. It is easy to see that the only realistic possibility is to threaten mate by Rg1. The immediate 1 Rg1? is no good due to 1...e2 (amongst other moves) and it follows that the key must be a move by the bishop on g3, so as to threaten Rg1. The main problem is to decide on the correct square. If the bishop simply disappeared from the board, Black would have defences, but it turns out that most of them already have a mate prepared. For example a random move of the c5-knight (to cover g1 with the bishop) is met by Qe4#, while 1...Nd3 2 Qxd7# and 1...Ne6 2 Qf5# deal with the two knight moves which prevent the mate on e4. Other lines are 1... Qd6 2 Qf5# and 1...f2 2 Qg2#; indeed, the only defence for which no mate is prepared is 1...Bb8. Therefore the key must be a move of the bishop which renders 1...Bb8 ineffective, while not interfering with any of the prepared mates. The first condition implies that the bishop must move in the direction of b8 (but not all the way, as 1 Bb8? allows 1...Bxb8!). 1 Bf4? Na4, 1 Be5? Ne6 and 1 Bd6? Nd3 all fail for the same reason: the bishop blocks the path of the queen to the mating square. Therefore, by a process of elimination the key is 1 Bc7!.} 1. Bc7 $1 (1. Be5 $2 Ne6) (1. Bd6 $2 Nd3) 1... Na4 (1... Ne6 2. Qf5#) (1... Nd3 2. Qxd7#) (1... Qxc7 2. Qf5#) (1... f2 2. Qg2#) 2. Qe4# *

[Event "Mate in three"] [Site "?"] [Date "1886.??.??"] [Round "?"] [White "Fison, Bernard"] [Black "The English Mechanic"] [Result "*"] [Annotator "John Nunn"] [SetUp "1"] [FEN "2Q5/1p2P1K1/pP2N3/r2kP1p1/q5R1/3p4/P2P3B/8 w - - 0 1"] [PlyCount "5"] [EventDate "1886.??.??"] {This rather old problem poses more of a puzzle and defeated a few strong solvers. The black king has no moves, and it is amazing that 1 e8Q doesn't mate in three, but it turns out that after 1...Qxg4 there is no way to finish Black off in two moves. One of the first things I noticed was a possible attractive mate by 1 Qd7+ Ke4 2 Nxg5#, which would also explain why there is a pawn on d2. For this to come about, the white rook must disappear and the black queen must be deflected to c4 to prevent Black meeting Qd7+ by ...Kc4. Sometimes you are lucky enough to hit upon a key clue quickly, and that was the case here. The only realistic way for the Qd7+ line to be realised is for the first move to be 1 Rc4 Qxc4. This puzzled me, because I couldn't see what White is threatening after 1 Rc4, and it was a few minutes before it occurred to me that Black might be in zugzwang after this move. Black doesn't have a wide range of moves, because many queen moves allow immediate mate by 2 Rd4#, and there are only a couple of lines which might cause a problem.} 1. Rc4 Qxc4 (1... Rb5 {blocks the b5-square and so allows} 2. Qd7+ Kxc4 3. Qd4# { incidentally explaining why there is a pawn on a2}) (1... Rc5 {is perhaps the hardest line, and is surprisingly met by} 2. Nc7+ {with three very attractive mates after} Kc6 (2... Kxc4 3. Qg4# {and}) (2... Rxc7 3. Qg8#) 3. Qe6#) (1... Qd7 2. Rd4+ Kxe6 3. Qxd7#) (1... Qb4 {is simply met by} 2. Rxb4) (1... g4 { gives access to f4 and is met by} 2. Nf4+ Kxe5 3. Qe6#) 2. Qd7+ Ke4 3. Nxg5# { works an anticipated} *

[Event "White to play and win"] [Site "?"] [Date "2016.??.??"] [Round "?"] [White "Nielsen, Steffen Slumstrup"] [Black "Original"] [Result "*"] [Annotator "John Nunn"] [SetUp "1"] [FEN "2K5/3B3n/8/8/8/4PN2/6p1/2k5 w - - 0 1"] [PlyCount "17"] [EventDate "2016.??.??"] {This was the first of the three studies and is relatively straightforward since there is one clear-cut line.} 1. Bh3 {Pretty much forced, or else Black draws by 1...Ng5, forcing Ng1, and then ...Kd2.} g1=Q {Otherwise the g-pawn falls and white wins easily with his extra material.} 2. Nxg1 Ng5 {Preventing the pawn's advance and intending ...Kd2.} 3. Bg2 {The correct square.} (3. Bf5 $2 {is wrong due to} Kd2 4. e4 Ke3 5. e5 Nf7 $1 ({not} 5... Kf4 $2 6. e6 { and White wins}) 6. e6 Nd6+ 7. Kd7 Nxf5 {with a draw as it takes too long to dislodge the black knight}) 3... Kd2 4. e4 Ke3 (4... Kd3 5. e5 Kd4 {transposes} ) 5. e5 Kd4 (5... Kf4 6. Nh3+ Nxh3 7. e6 Ng5 8. e7 Nf7 9. Kc7 {wins for White}) 6. Nf3+ Nxf3 7. e6 {The same idea as in the previous note, but this time Black has an additional possibility} Nh4 8. Be4 $1 {The final twist.} (8. e7 $2 Nf5 { only draws due to the fork on d6}) 8... Kxe4 {Black has no choice, as his knight is immobilised} 9. e7 {and wins because now the pawn promotes with check.} *

[Event "Helpmate in 3 (3 solutions)"] [Site "?"] [Date "1993.??.??"] [Round "?"] [White "Grubert, Harald"] [Black "Phénix"] [Result "*"] [Annotator "John Nunn"] [SetUp "1"] [FEN "4q1rB/8/n6K/p1k5/R2p1p2/2n1P3/8/7b b - - 0 1"] [PlyCount "6"] [EventDate "1993.??.??"] {As usual in helpmates, it is all about identifying the mating position(s). It helps to be familiar with the typical mating structures with various combinations of white material. Here we have a rook and a bishop (plus a pawn, but let's ignore that for a moment). The most economical arrangement for mating in the middle of the board with the R+B combination is when the rook, bishop and enemy king all lie on one diagonal, for example bishop on b1, rook on f5 and enemy king on e4. This only requires two additional squares to be covered, e3 and d4, whereas all other arrangements require at least three additional squares to be covered. When I think there might be a rook+bishop mate, I always look first for this type of arrangement, and here there's an obvious possibility, namely rook on b6 and bishop on d4. Thanks to the white pawn, this will be mate if c4 and d5 can be blocked. d5 can be blocked in one move by ...Nd5, leaving two moves to block c4, a task which must be accomplished by a knight of a bishop (or else it is not mate). This immediately gives a solution: 1...Bd5 2 Rb4 Bc4 3 Rb6 Nd5 4 Bxd4#. Another typical helpmate solving idea is to look for the point of the problem. Here we have seen a mate with Bd4 and, if we note that there are three solutions and three possible white pieces which can move to d4, a reasonable guess is that the other two solutions will end with the rook and the pawn moving to d4. Is it possible to mate with exd4? There are five squares to be covered with the remaining moves, but notice that three of the squares, at b5, c6 and d5, can be occupied by black blockading pieces in a single move. That only leaves two squares, b6 and d6, to be covered by White's two remaining moves. This can be achieved by playing the bishop to c7, giving the second solution 1...Qb5 2 Be5 Bc6 3 Bc7 Nd5 4 exd4#. That only leaves the mate with Rxd4, and it's reasonable to suppose that the black king will move to d5, leaving c5, c6 and e6 to be covered (or blocked) by the remaining two white and two black moves. c6 and c5 are no problem as Black can block these in one move each, but e6 cannot be so blocked as ...Qe6 would check the white king. However, there are two white moves left to deal with the e6 problem, just enough to solve it by exf4 and f5. This gives the third solution 1...Bc6 2 exf4 Kd5 3 f5 Nc5 4 Rxd4# } 1... Bd5 (1... Qb5 2. Be5 Bc6 3. Bc7 Nd5 4. exd4#) (1... Bc6 2. exf4 Kd5 3. f5 Nc5 4. Rxd4#) 2. Rb4 Bc4 3. Rb6 Nd5 4. Bxd4# *

[Event "Mate in four"] [Site "?"] [Date "1943.??.??"] [Round "?"] [White "Heathcote, Godfrey"] [Black "American Chess Bulletin"] [Result "*"] [Annotator "John Nunn"] [SetUp "1"] [FEN "r1nrb3/5pN1/8/1pQpN1P1/4kp1B/p1p5/P4P2/4K3 w - - 0 1"] [PlyCount "7"] [EventDate "1943.??.??"] {This was the toughest in the whole set of moremove problems to solve, and was certainly the toughest to give a complete solution. In the world championship, many of the top solvers (myself included) overlooked a variation or gave an incorrect continuation. One reason the problem is difficult is that it is not obvious what the point is. The black pieces appear very out of play and the black king is subject to the attack of a large white force, but it's not easy to mate, mainly because in the diagram Black has the strong defence ...Kxe5, for which no mate is provided. My approach was to look for a nice mate and see how I could make it come about. A queen sacrifice is always appealing, so I started to wonder about Qe3+ followed by f3+. If one imagines that e5 is covered and the black f-pawn has moved, then there is a very nice mate if Black meets 1 Qe3+ fxe3 2 f3+ by 2...Kd4, since then 3 Ne6# is possible. This would also provide a use for the c3-pawn. The only first move which might make this work is 1 Bg3 and a quick check showed that if, for some reason, Black moved his f-pawn then 2 Qe3+ does indeed function as intended. When I noticed that 1 Bg3 deals with 1...Kxe5, since then 2 Bxf4+ Kxf4 3 Qe3+ Kg4 4 Qg3 is mate, I was certain that I had found the correct first move. But I could not see what the threat was, nor could I work out why Black should move his f-pawn. Curiously, I was able to work out almost all the variations without knowing the threat, but to cut a long story short I finally noticed the threat of 2 Qxc3 (intending 3 f3#) 2...d4 3 Qf3+ Kxe5 4 Bxf4#. A quiet (non-checking) threat always adds to the difficulty of a problem and here the rather slow threat gives Black several possible defences, many of which lead to attractive continuations.} 1. Bg3 f6 {Meeting the threat since now 2 Qxc3? can be answered by 2...Bh5!. Note that 1...f5 leads to the same continuation.} (1... -- 2. Qxc3 d4 3. Qf3+ Kxe5 4. Bxf4#) (1... Ra4 2. Qxc3 Rd4 (2... d4 3. Qf3+ Kxe5 4. Bxf4#) 3. Qe3+ fxe3 4. f3# {a second attractive queen sacrifice line}) (1... Kxe5 2. Bxf4+ Kxf4 3. Qe3+ Kg4 4. Qg3#) (1... Bd7 {intending to meet 2 Qxc3 by 2...Bg4} 2. f3+ Kxe5 3. Qb4 {threatening mate by taking on f4} d4 (3... fxg3 4. f4#) 4. Qc5# {which only works because the bishop on d7 blocks the rook from interposing on d5}) (1... c2 2. Qxc2+ Kxe5 3. Bxf4+ Kxf4 (3... Kd4 4. Nf5#) 4. Qf5#) (1... b4 2. f3+ Kxe5 3. Bf2 {followed by} -- 4. Bd4# { exploiting the fact that the pawn on b4 prevents the defence ...Ra4}) 2. Qe3+ fxe3 3. f3+ Kd4 4. Ne6# *

[Event "Selfmate in three"] [Site "?"] [Date "2003.??.??"] [Round "?"] [White "Degener, Ugo"] [Black "3rd Comm. Buletin Problemistic"] [Result "*"] [Annotator "John Nunn"] [SetUp "1"] [FEN "rb6/8/3P1N2/3pP3/Q5Br/1p1kN1R1/1Pp5/KbB1R3 w - - 0 1"] [PlyCount "5"] [EventDate "2003.??.??"] {It's immediately obvious that White must force Black to mate along the a-file, but it's less clear how this can be accomplished. 1 Qa6+ is a possible idea, but at the moment d4 is not covered so Black can just reply 1...Kd4. For me, the big clue in the diagram is the formation of pawns on e5 and d6. Why are they there? It seemed to me that one possible way to force Black to mate is by 1 Nc4+ Kd4 and then a discovered check forcing Black to take the queen. At the moment this doesn't work because c5 is not covered, but if White's first move guarded c5 then the threat would be 2 Nc4+ Kd4 3 Nd2+, forcing 3...Rxa4#, with the white pawns preventing the alternative third moves 3 Ne5+ and 3 Nd6+. This immediately narrowed the choice down to 1 Ne4 or 1 Nd7, and I saw at once that 1 Ne4 would not work because after 2 Nc4+ Kd4 3 Nd2+ Black could play 3...Kxe5. With the key settled, it only remained to work out the variations.} 1. Nd7 Ba7 {the two most obvious defences are the bishop moves blocking the a-file} (1... -- 2. Nc4+ Kd4 3. Nd2+ Rxa4#) (1... Ba2 2. Nxc2+ Kxc2 3. Qxb3+ Bxb3#) (1... Rxg4 {1...Rh3 is met the same way} 2. Nf5+ {this works because it no longer mates Black} Rxg3 3. Qa6+ Rxa6#) (1... d4 2. Bf5+ Re4 3. Qa6+ {exploiting the self-block of d4 by the black pawn} Rxa6# {In these last two variations, the first idea of arranging Qa6+ comes to life.}) 2. Qc4+ {a surprising queen sacrifice to clear the a-file with gain of tempo} dxc4 3. Nf5+ {the correct square, preventing ...Kd4} *