Chess Problems: The Self-block problem solutions

[Event "1st HM Theme Tourney No.11 idee & form"] [Site "London"] [Date "1986.??.??"] [Round "?"] [White "Touw Hian Bwee"] [Black "Mate in 2"] [Result "*"] [Annotator "David Friedgood"] [SetUp "1"] [FEN "8/1p4p1/8/1QPN1RK1/3Pk1p1/1n2p3/2PrRP2/b1q2b2 w - - 0 1"] [PlyCount "3"] [EventDate "2012.??.??"] {It is generally a good idea, when solving a problem, to take account of the black monarch's situation. Here we see that the king has a flight square on d4, so that the threat introduced by White's first move (the 'key' move) needs to guard this square in addition to giving check. The threat of 2.Rf4# is easy to find, but to make it work a move of the Nd5 first is needed to guard d5, which is relinquished by the rook when moving to f4. The knight has a full 'wheel' (all 8 possible moves) available, but the two checks on f6 and c3 allow it to be captured, while 1.Nf4? obstructs the rook from playing to that square. So which move of the knight is the key? Did you settle on} 1. Nc7 $1 {rather than fall for one of the following:} (1. Ne7 $2 Rxd4 $1 {as now the knight interferes with mate by} 2. Qe8) (1. Nxe3 $2 Nxd4 $1 {as now the knight obstructs 2.Rxe3#}) (1. Nb6 $2 Bxd4 $1 {as now 2.Qxb7# is impossible}) (1. Nb4 $2 Kxd4 $1 {as now 2.Qb4# is impossible}) 1... Kxd4 {is thematic:} ({Any capture of the Pd4 will defeat the threat by making e5 a potential flight square. However, each of the three captures by a piece also blocks d4, enabling White to mate by being careful:} 1... Nxd4 2. Rxe3# {and not} (2. Qe8+ $2 Ne6+ $1 {the self-blocking piece itself wards off the check}) ({nor} 2. Qxb7+ $2 Nc6 $1 {and again the self-blocking piece itself wards off the check}) ) (1... Bxd4 2. Qxb7# ({and not} 2. Qe8+ $2 Be5 $1) (2. Rxe3+ $2 Bxe3+ $1)) ( 1... Rxd4 2. Qe8# ({and not} 2. Rxe3+ $2 Qxe3+ $1 {as Black's first move has opened the queen's line to e3}) ({nor} 2. Qxb7+ $2 Rd5 $1)) 2. Qb4# {This problem combines three self-blocks on a single flight square with four tries [attempts at solution each refuted by a unique defence], each one refuted by a different thematic defence. It is shown with the crystal clarity typical of this composer, with some constructional features requiring considerable ingenuity.} *

[Event "2nd HM De Waarheid"] [Site "London"] [Date "1976.??.??"] [Round "?"] [White "Touw Hian Bwee & H Maruta"] [Black "Mate in 3"] [Result "*"] [Annotator "David Friedgood"] [SetUp "1"] [FEN "8/2K1N3/p2BPr2/4p1bN/1pbk1p2/3P3B/p2Q4/8 w - - 0 1"] [PlyCount "5"] [EventDate "2012.??.??"] {I trust that, after the hints I gave, the key move wasn't difficult to find:} 1. Bf1 {threatening (see below)} -- ({The following defences each lead to anticipatory self-blocks (i.e. blocking a flight exploited by White not immediately but on the third move):} 1... Bb5 2. Bc5+ $1 Kxc5 3. Qf2#) (1... Bb3 2. Qf2+ Kc3 3. Bxe5#) (1... Bxe6 2. Bxe5+ $1 Kxe5 (2... Kc5 3. d4#) 3. Qb2# ) (1... f3 2. Qb2+ Ke3 3. Bc5#) ({The following variation is not part of the thematic content of the problem:} 1... Bd5 2. Nxf6 Bxe6 (2... -- 3. Nf5#) (2... Be4 3. dxe4#) 3. Nc6#) 2. dxc4+ Ke4 3. Qd3# {This remarkable problem combines 3 themes. Firstly, we have the anticipatory self-blocks, which provide the bedrock on which the other themes are constructed. Secondly, the squares to which the black king is lured on the second move (c5, c3, e5 and e3) form what are called 'starflights'. Thirdly, and most modernistic of the three, the white second and third moves form a fourfold cyclic pattern, as follows: Let Bc5 be denoted by A, Qf2 by B, Bxe5 by C and Qb2 by D. Then, the pattern formed by the thematic variations set out as above are: 1...Bb5 2.A 3.B 1.. . Bb3 2.B 3.C 1...Bxe6 2.C 3.D 1...f3 2.D 3.A This is all achieved with relatively good economy, the only really jarring components being the black pawns on a6 and a2, which prevent the black bishop from defending with impunity. Prodigious ingenuity must have been deployed to arrive at this deceptively laid-back problem!} *