Problems from La Scacchiera Invisibile

1.Rd7 Nxd7 2.Nc6, then after any knight move, 3.Nf6#. Ciancarini notes that, considered as a Kriegspiel position, this is not very interesting because White needs no information from the referee.

The orthodox key is 1.b8=N. The main lines are 1...Kc7 2.f8=Q Kb6 3.Qc5# and 1...Ka7 2.f8=Q Ka8 3.Nc6#. In Kriegspiel this cannot be solved in three, because White cannot distinguish the two black replies, which require different third moves. The Kriegspiel solution is 1.b8=N Kc7/a7 2.f8=Q Kb6/a8 3.Qc8 Ka7 4.Nc6#.

The key is 1.Rg3, threatening 2.Rxd3#. The defenses are ...fxg3, ...dxe2, ...Rxf1, ...Bf3, ...Rc3, ...f3, ...dxe4, and ...Bxe4. The first three captures are unambiguous and reveal the mate. Against the silent defenses ...Bf3, ...Rc3, and ...f3, White tries 2.Kf3#, then 2.Ke1#, then 2.e3#; the first accepted move mates. The real difficulty is distinguishing ...dxe4 from ...Bxe4, which require different mates in orthodox play. Swart explained that Dutch rules announce whether a capture is made by a pawn or by a piece, so the referee distinguishes "Black captures on e4 with a pawn" from "Black captures on e4 with a piece." Ciancarini concludes that the problem is therefore solvable only with Dutch rules, while the extension is acceptable for problem composition.

1.Ra1+. If the referee says "Black captures on a1," the promotion was to queen or rook, and 2.Bc2# follows. If the referee says "Black has moved," Black must have played 1...Kb3, so 2.Ra3#.

White cannot reconstruct the black king's position exactly. Black's exchange with the referee reveals a black pawn on g2. The black king could only have been on a8 or e4, and may have moved to b8, e3, or e5. In every possible reconstruction, 1.Qe8# mates.

After 1.Qe3, Black could answer 1...Rfe6; the referee would only say "Black has moved," and White could not be sure of mating. The right move is 1.Qe7. After Black moves, White tries 2.Qxe2#; if that is illegal, one rook has interposed, so White tries 2.Qxh4#; if that is also illegal, Black has played 1...Rbe6, and 2.Qb4# is certain.

1.Bh1. If the referee says "Black captures" (1...Nxe1, 1...Nxh1, or 1...Nxh3), play 2.Qe4#. If the referee says "Black has moved," ask "Are there any?" If the answer is "Yes," try the impossible capture 2.dxe3, then play 2.Qe4#. If the answer is "No," try 2.Qe6#; if that is illegal because of 1...Ne4, play 2.Qxe4#.

1.Kc1. After Black's move: if the referee says "capture on d6" (1...Rxd6), play 2.Bxf5#; if the referee says "capture on h8" (1...Bxh8), play 2.Qh6#; if the referee reports no black capture, White asks "Are there any?" If "No," the black rook has moved, so 2.Bxf5#. If "Yes," try 2.gxf6#; if that is refused, Black has played 1...Bh6, pinning the pawn, so 2.Qxh6#.

1.Kh8. If the referee announces "Black moves and gives diagonal check" (1...Bd4+), play 2.Re5#. If the referee is silent, try 2.Rxb3#. If that is refused because the black pawn did not move, play 2.Qd5#.

1.Qa3. Then try 2.Rg5#. If the bishop on d5 has not moved, 2.Rg5 is refused; try 2.Qe3#, which mates if the black king moved to e5. If the black pawn moved to c3, play 2.Qxc3#.

The set play, if Black were to move, is 1...Bf3+ 2.Rg4#, 1...d2 2.Rxd2#, and otherwise 2.Qf4#. The key is 1.Qb2. Now 1...B moves is met by 2.Rg4#; 1...Kf4 by 2.Qf2#; and 1...d2 by 2.Qxd2#.

1.Rc1. If Black captures the rook, first try 2.Qb5#, which mates if the capture was made by the pawn on b2. If 2.Qb5 is refused, the knight made the capture, so 2.Nf4#. If the referee does not announce the rook's capture, ask "Are there any?" If "Yes," try cxb4, then play Nf4#. If "No," try 2.Qf5#; if that is illegal, try 2.Rh1#, which mates if Black promoted the h2-pawn. If 2.Rh1 is also illegal, Black played 1...Ng1, so 2.Nf4#.

1.Bf6. If the referee announces the bishop's capture, play 2.Qe3#. If there is no announcement, ask "Are there any?" If "Yes," make the empty try 2.dxe5, then play 2.Rc4#; if 2.Rc4 is refused, play 2.Nb5#. If "No," try 2.d5#; if refused, try 2.Rc4# or 2.Qc2#.

1.Rg8. If the referee announces "knight check" (1...Nf3+), play 2.exf3#. If no check is announced, ask "Are there any?" If "No," play 2.Bxf5#. If "Yes," make the empty try 2.hxg7, then play 2.Rg4#; if 2.Rg4 is refused, play 2.Bf5#.

1.Bh1. If there is no announcement, 2.Nd5#; otherwise 2.Ne4#. Why are 1.Bb7, 1.Bc6, 1.Bf3, and 1.Bg2 not just as good? Anderson leaves that as an exercise.

1.Rf2. If 1...Bxf2, play 2.Qxg5#. If 1...Nf3+, play 2.Bxf3#. If the referee is silent, ask "Are there any?" If "Yes," use 2.exd5 and then 2.Bf3#. If "No," Black has played 1...Bg3, so 2.Qxg5#.

1.Na3. After Black's move, first try 2.Qg5#; only if that move is not playable, because of 1...Nf6, finish with 2.Qd2#.

1.Bb1. With a silent referee, try 2.Qg8# first, then 2.Qb5#.

1.Nc5. If there is no announcement, first try 2.Qb1#, then 2.Qh7#.

1.Qg2, threatening Qe4#. The only defenses are ...exd5 and ...Kf5. The first is revealed by the referee's "capture on d5" announcement and is met by 2.Qc2#. The second is discovered by trying 2.g6, legal only if the black king has moved; it mates by discovered check. Notice that 2.Qc2 is not a threat, because it is parried by the silent move 1...e5.

1.Kh2. Black makes a silent move, either 1...c5 or 1...Nc2; White tries, in order, 2.Bb1 and then 2.Bd3+.

1.Kc7. If 1...b1=B or 1...b1=N, play 2.Kb8. If 1...b1=Q or 1...b1=R, play 2.Bc3+.

1.Bh8. If 1...bxa1=R or 1...bxa1=N, 2.Kg7 is playable. If 1...bxa1=Q or 1...bxa1=B, play 2.Bxc2+ and 3.Qb3#.

1.Ba8. A capture, 1...Nxe3, is met by 2.Rd2#. If "Are there any?" is answered "Yes," 1...f4 is met by 2.Be4#. If the answer is "No," the relevant lines are 1...Nd4 2.Qd1#, 1...Nc6 2.Qxc2#, and 1...Nd5 2.Qxc2#.

1.Kf3. The lines are 1...Nd8+ 2.b7#, 1...f6 2.Ne6#, 1...f5 2.Ne6#, 1...Kd4 2.Qe3#, and 1...c3 2.Qxc3#.

1.a6. If 1...Nd7, play 2.Rf6. If 1...Nxa6, play 2.Rf5.

1.Nd5, threatening 2.Nxd3. The lines are 1...Rxd5 2.c4+, 1...Rd4 2.c3+, 1...Rc3 2.Nxc3+, 1...Rb3 2.cxb3+, and 1...R(N)xd2 2.Nb4+. This is a complicated problem in which the main actor is the pawn on c2. Wherever the rook on d3 moves, the c-pawn follows it, so that if Black captures the rook on d2 on move two, White can ask "Are there any?" and mate with 3.Qc2# if the answer is "Yes," otherwise 3.Qb1#.

1.a3 d6 2.a4 h6 3.a5 h5 4.a6 h4 5.a7 N any. Before each pawn move, White systematically tries Qf5 to make sure the knight has not moved. After Black's fifth move, White asks "Are there any?" If "Yes," White makes the empty try 6.axb8, then plays 6.Qf5#. If "No," White plays 6.Qh5#.

1.f8=N. White then asks "Are there any?" If "Yes" (...Qb8), try dxc5 and play 2.d5 Kc5 3.Nd7#.

1.b4, threatening 2.Qb6. If 1...Bxb4, play 2.Qh6; if 1...axb3, play 2.Qxc3; if 1...Bxf1 or the rook on a5 moves, play 2.Qc5.

1.b4, threatening 2.Nc5+. If 1...Bxb4, play 2.Qh6; if 1...Bxf5, play 2.Qc3.

1.Rd1, threatening 2.Re1 and 3.Bxe3#. The only two defenses, 1...e6 and 1...e5, are both silent; they are not immediately distinguishable by asking "Are there any?" because of en passant. The strange rook sacrifice on f1 exists precisely to lose the right to capture en passant and let White use the question meaningfully. After 1...e5, play 2.Rf1+ gxf1=Q 3.Any? no Rg4#. After 1...e6, play 2.Rf1+ gxf1=Q 3.Any? yes Qf7#.

1.Ka1, threatening 2.Nd6+. If 2...Ke5, then 3.Rxe6#; if 2...Rc4, then 3.Rxb5#. Other lines: 1...e5 2.Rd6+ cxd6 3.Qg8#; 1...Bxf6+ 2.Nb2+, and then if 2...Ke5, 3.Nd3#, while if 2...Rc4, 3.Rxb5#.

1.Nb5, threatening ...c5 2.Nxc7+. If 1...cxb5, play 2.Bg2+; if 1...gxf5, play 2.Qe6+ (White discovers which piece captured on f5 by asking "Are there any?"); if 1...Rxf5, play 2.Qe4+; if 1...Bxf4, play 2.c4+.

1.f8=N Kxc6 2.Nd7. If 2...Kxd7, then 3.Bxb5#; if 2...Kd5, then 3.Bb7#. The promotion to a knight, which is then brought to d7, serves only to distinguish the two possible second moves of the black king from c6.

1.Rd3, threatening 2.Ne6+. If 1...Qxb3, play 2.Nc6+. If 1...Qxd3 or 1...Qxg1, play 2.Rb6+.

1.Qc5, threatening 2.Raf6 and 3.Rxf8#. If a knight moves, 2.Bf6 and 3.Rh6#. If 1...c6, 2.Nf6 threatens 3.Nf7#.

1.Bd4, threatening 2.Rh1+. If 1...cxd4, play 2.Qa5; if 1...Rxd4, play 2.Qxc5; if 1...e3, play 2.Qd5.

1.c4, threatening 1...Bg4 2.O-O Bh3 3.Rae1 Bxf1 4.Ng6#. If 1...Bxe8, play 2.O-O-O Ba4 3.Rhe1 Bxd1 4.Ng6#.

1.Kg5 2.Kf4 3.Ke5 4.h5 5.h6 6.h7 7.h8=Q or R Nc4+ 8.Kf4, then 9.Rxc7#. Meanwhile Black either moves the bishop between g1 and h2 or moves the knight, which at most gives a check on c4.

1.Be7 2.Bf8 3.Bh6 4.Bg7 5.Bf8 6.Be7 7.Bd8. Seven moves recreate the initial position with Black to move. More precisely, after the maneuver either Black has captured the bishop, making a knight mate easy, or the black bishop is on c7 or a7. Black's seventh move is therefore either 7...Bxd8, a capture that is announced, or 7...Bb8, not announced. White plays respectively 8.Nxd6 or 8.Nxb6, both followed by 9.Nc4#.

1.Nc4, threatening Qxb6#. The lines are 1...N8xd7 2.b8=Q#; 1...N6xd7 2.Nxb8#; 1...Nc8 2.dxc8=N#; 1...Na8, 1...Nd5, 1...Nxa4, or 1...Nxc4, all met by 2.Bxb8#; and 1...Kxb7 2.Nc5#.

1.Re3. If 1...Rb8, play 2.cxb8=B e4 3.Bh2 B any 4.Bg3#. If 1...Ra8, 1...Rc8, 1...Rd8, 1...Re8, or 1...Rf8, play 2.Qf3 B any 3.Nxf6+ Kh4 4.Qg4#. If 1...Rg8 or 1...e4, play 2.Rxe4 any 3.Qf3 any 4.Nxf6#.

1.Rg2, threatening 2.Bf4 3.B(x)h6 4.Bg5#. If 1...e5, play 2.Bg1 f4 3.Be3 fxe3 4.Rg4#. If 1...Kxh3, play 2.Rg3+ Kh4 3.R3g1 any 4.Bf4#.

The reconstruction is the hard part. A black king on g6 has six attempts. Add two black queens on a1, a8, or h8 and each can have at most six refused attempts along files occupied by white pieces: 18 total, not 19. Black therefore needs pieces capable of at least seven refused attempts. Two rooks, unlike two queens, get seven refusals each if they try to castle with a king on e8; the king itself supplies five. The reconstructed position is r3k2r/N3P2R/4K3/7N/8/8/P7/8 w - - 0 1. White asks "Are there any?" If "Yes," he tries axb3 and plays 2.Ng7#; if "No," he mates with Nf6#.

This is very difficult, partly deduction and partly trial and error. The 18 refused attempts must concern the king, which accounts for eight and therefore cannot move; pawn captures, which account for three and therefore capture nothing; and seven queen attempts, because otherwise it is hard to see how seven knight or bishop moves could all be refused. The refused queen tries should be Qg8, Qf7, Qe6 and Qh4, Qg4, Qf4, Qe4, revealing respectively a black queen on d4 and bishop on d5. For mate in one, the black king must be on d8. The reconstructed position is 3k4/8/3K2B1/3b1P2/1PQq4/5N2/8/8 w - - 0 1, and the mate is 1.Qc7#. Anderson notes that in the twin problem obtained by shifting the position one file to the right, the number of refused tries is only 17.

The refused attempts must concern the king, eight attempts; the queen on a7, b6, h8, g7, and f6; three pawn-capture attempts; and two pawn-push attempts. The reconstructed position is 8/8/4K1kB/3q1nP1/2PQ4/6N1/8/8 w - - 0 1, and 1.Qe4# mates.

1.Kd3. Then 2.Kc4# against ...Kd6, sor 2.Kd4# against ...Kb5, sor 2.Qe5# against ...Kd5. All defenses are silent. The same solution works under both English and American rules.

1.Rb5. Non-silent: 2.Kxb5# after cxb5, or 2.Re5# after Nxc7. Silent: 2.Kxd4# after Re3, or 2.Kxd3# after Nf3 or Be3, sor 2.Re5# after a3, d2, g5, Nf5, Ng2, h1, Rf3, Rg3, or Bf2, sor 2.Kxc5# after Nc5, sor 2.Rb6# after c5.

1.Rc8. The Eastern and Western rule continuations are both part of the solution. Under Eastern rules, the non-silent continuations are 2.dxc3# after Nc3, or 2.Rc4# after Rxf3, Rxd7, or Bxa7. If Any? is "Yes," 2.dxe3# after Ne3, sor 2.Qa1# after Nc5, sor 2.Rc4# after Rf6, Rg7, Nf6, Nf2, Nh2, or Nh6, sor 2.Ne7# after Bc5. If Any? is "No," 2.Qxb6# after Nb2. Under Western rules, with zero possible captures, 2.Qxb6# follows Nb2; with one possible capture, 2.dxc3# after Nc3, or 2.Rxd5# after Rxd5, or 2.Qa1# after Nc5, sor 2.Rc4# after Rxf3, Rxd7, Rf6, Rg7, Nf6, Nf2, Nh2, or Nh6; with two possible captures, 2.dxe3# after Ne3, sor 2.Ne7# after Bc5.

1.Be3. Non-silent: 2.Qd5# after dxe3, sor 2.Rc1# after Bxe3, sor 2.Rh5# after Rxe3. Silent: 2.Qxd4# after Bf2, sor 2.Bxd4# after Rf2.

1.Kd2. Non-silent: 2.KxQ# after a queen move, or 2.Kxd3# after Rxd3, or 2.Kxc3# after bxc3, or 2.Qc2# after Nxf4. Silent: 2.Qc2# after any move.

1.Qc1. Non-silent: 2.Nxc4# after Qc4, or 2.Kxb3# after Qxb3, or 2.KxQ# after a queen move on the d-file, or 2.Nxe4# after Qxe4, or 2.Qa3# after Qxd6, Qxe6, or Nxe4. If Any? is "Yes," try 2.bxa6, then 2.Qa3#. If Any? is "No," 2.Nb7# after Qd4, Bd4, or Bb7.

1.c4. Non-silent: 2.Bf3# after dxc4, or 2.Rh4# after dxc3. Silent: 2.Qh8# after d3, sor 2.Qxe2# after any bishop move, sor 2.N1g3# after any knight move. The orthodox keys Bxd5, Bc6, and Qb5 fail because silent black knight moves require different mates.

1.Qe6. Non-silent: 2.Rxc3# after Bxc3, or 2.Qxe4# after Nxe4, or 2.dxc6# after bxc6. Silent: 2.d6# after Nc8, Ne8, Nf7, or Nf5, sor Any? yes, make the empty try 2.bxa5, then 2.Ne5# after f5; if Any? is "No," 2.Nb2# after Bb2.

1.Nf4. Non-silent: 2.Nc6# after Rxf4, or 2.Rxd5# after Bxh5, or 2.d4# after Kxe5. Silent: 2.Nxf3# after b5, any bishop move, or any rook move. 1.Ne1 and 1.Ne3 are not acceptable because silent rook moves require different mates.

1.b5. Silent: 2.Qc6# after Ba7, Nc1, Ne1, f3, e4, Rd5, Re4, or Ra4, sor 2.Bxc7# after Bc5, sor 2.Qxe5# after Rc4, sor 2.Nc4# after Nc5. Non-silent: 2.Qc6# after Bxa5, Nxb2, or Nxb2. With one possible capture: 2.Rd7# after c6 or c5, or 2.Qxe5# after Rb4, sor 2.Ne4# after Nb4.

1.Nd6. Non-silent: 2.Qa1# after Bxb3, or 2.Rd5# after hxg6 or Nxd6, or 2.Qxe5# after Qxe5, or 2.Qb4# after Bxf2, Qxf2, Nxh6, or Qxh6. Silent: 2.Qa1# after Bc2, Bf3, Bg4, or Bh5, sor Any? yes, try axb6, then 2.Nb5# after Ng7, Ne3, Ng3, or Qg3; if Any? is "No," 2.Qb4# after a6, sor 2.Qxd2# after d2. 1.Na3 fails because of 1...Nd6.

1.Ne3. Non-silent: 2.f4# after Nxe3, or 2.N3c4# after Rxb8, or 2.Qe8# after Bxd6, or 2.Ng4# after Bxg5. Silent: 2.Ng4#. 1.Nd4 fails because it threatens three different mates with different silent defenses.

1.Bxd4. Then 2.Kxd6# after c6 or c5, or 2.Kf6# after g6, or 2.Kd7# after Bd7, Bg6, or Bh5, or 2.Kf7# after Bf7, Bc6, Bb5, or Ba4, or 2.Kf6# after g6, sor 2.Re3# after Nb2, Nf2, or Ne3. 1.Rf1 fails because the silent defenses 1...Ne3 and 1...Nf2 require different mates.