White pawns captured at least 14 times. But no one of them could have captured on a-file and as white has 16 pieces, Black can have pawn on a4, a5, a6 or a7. That's why white must set a question: "Are there any?"

- if the answer is "yes", it means Black has a pawn. Black ing can be on d2, f6, h6, f7, h7, d8, e8, g8. Then white tries any stupid capture, e.g. c2xd3 to fulfill rule, it is of course impossible, afterwards 1.g8Q! without stalemate as Black has pawn. With bK on d8, e8 it is immediate mate, in other cases 2.Q4g5#. If 1.g8Q impossible (=> bKg8), then 1.Qg6! 2.Bd5#.

- if the answer is "no", Black has no pawn. Black king can be on the same squares except d2 as in this case Black has no last move. 1.g8R! with 2.Qg6#. If 1.g8R impossible (=> bKg8), then 1.Qg5! 2.g8Q#.

The key is the same in all 3 positions 1.Qe4!, there are 3 threats (potential mates) that can be defended by Black: 2.Qxe7#, Qa8#, Bf7#. After black move, white must be very careful.

In a): White cannot try 2.Bf7? as black could have played 1...Qe5! nor 2.Qa8? because of 1...Qa3! So 2.Qxe7#! If impossible, then not 2.Bf7? yet (1...Qe5!), but 2.Qa8#! If impossible, then it is clear Black move was 1...Qd3 or Qc2 and 2.Bf7#! is OK.

In b): White cannot try 2.Qxe7? because of 1...Sc6! nor 2.Bf7? as black could have played 1...Qe5! So 2.Qa8#! If impossible, then not 2.Qxe7? yet (1...Sc6!), but 2.Bf7#! If impossible, then it is clear Black move was 1...d5 and 2.Qxe7#! is OK.

In c): White cannot try 2.Qa8? as b-file is opened nor 2.Qxe7? because of 1...Sc6! So 2.Bf7#! If impossible, then not 2.Qa8? yet (1...Qb3!), but 2.Qxe7#! If impossible, then it is clear Black move was 1...Re6 and 2.Qa8#! is OK.

Cycle of three white tried mates in three positions: ABC/BCA/CAB.

1.Bxc3! with 3 potential mates: 2.Rf1#, Rb2#, Bxd3#. The way white will continue depends on judge.

- if no announcement by judge, then 2.Rf1#!, if impossible, 2.Rb2#!, if impossible (1...Bf2), 2.Bxd3#!

- if "capture on h5" is announced, then 2.Rb2#!, if impossible, 2.Bxd3#!, if impossible (1...Rxh5), 2.Rf1#!

Cycle of moves tried by white depending on announcement.

-if "capture on c3", 2.Rf1#,

-if "capture on e3", 2.Rb2#,

-if "capture on h2", 2.Bxd3#,

Mates reappear once more.

The key is the same in all 3 positions 1.e6!, there are 3 threats (potential mates) that can be defended by Black: 2.Bf6#, Rxd7#, Qb8#. After black move, white must be very careful.

In a): White cannot try 2.Qb8? as black could have played 1...Rc3! nor 2.Rxd7? because of 1...Qc7! So 2.Bf6#! If impossible, then not 2.Qb8? yet (1...Rc3!), but 2.Rxd7#! If impossible, then it is clear Black move was 1...Sd4 and 2.Qb8#! is OK.

In b): White cannot try 2.Bf6? because of 1...Qa1! nor 2.Qb8? as black could have played 1...Rc3! So 2.Rxd7#! If impossible, then not 2.Bf6? yet (1...Qa1!), but 2.Qb8#! If impossible, then it is clear Black move something to d6 and 2.Bf6#! is OK.

In c): White cannot try 2.Rxd7? because of 1...Qc7 nor 2.Bf6? because of 1...Qa1! So 2.Qb8#! If impossible, then not 2.Rxd7? yet (1...Qc7!), but 2.Bf6#! If impossible, then it is clear Black move was 1...Re5 and 2.Rxd7#! is OK.

Cycle of three white tried mates in three positions: ABC/BCA/CAB.

White must avoid a move to black square that would capture black bishop or in some positions move that would allow black bishop to capture movig white piece. 1.Rg2! (if impossible, then 1.Sf2#) 2.Rg8 (if impossible, then 2.Be5! 3.Rxh2+ Bxh2 4.Sf2#) 3.Rh8! (black bishop cannot be on h8 as it would have to be on g7 before that and it's impossible) 4.Rh5 5.Rb5 (if impossible, then 5.Rh3 6.Be5) 6.Rb1 7.Sf2+ Bxf2 8.Kxf2#. White rook must visit h8 on its passage from a2 to b1, very exciting idea!

White pawns captured 15 times, that's why Black has already only lone King. He can be placed on d4, f6, h2, h8, c8, d8, e8, f8. Black, beeing on move, would be mated immediately: 1...Kxh3, Kxd3, Kxg6, no announcement 2.Rh1#, Qd5#, Qe6#, Qa8#. But...

White has to move first! He cannot maintain all variations and changes two of them. After key 1.Rh7!! black reveals position of his king: 1...Kxh3, Kxd3, Kxg6, no announcement 2.Rh1#, Qd5#, Qf7#! (Qe6+? Kxh7!), Rh8#! (Qa8+? Kxa8!). Tries: 1.Rf7? no announcement!, 1.Qg8? stalemate with Kf6!

White pawns again did 15 captures and Black has only lone King. He can be on a1, b1, c1, d1, e1, c4, c6, h5, h7, h8, but not on h1 as Black lacks last move in this case! Tries: 1.d8Q? stalemate with Ke1!, 1.c8Q? stalemate with Kc4!, 1.b8Q? stalemate with Ka1!, solution: 1.a8Q!, if it was "check on horizontal line", then 2.Qg7#, normal variations: 1..."no announcement", Kxc5, Kxc7, Kxd7, Kxh6 2.Qg1#, Qc3#, Qc8#, c8Q#, Qh8#.

1.Rg4!! - shocking key throwing own king under attack of black battery, preparing two mates by double check - 2.Sbd4#, Sed4#. Now the way of things depends on judge:

- "no announcement" - White mustn't ask "Are there any?" as he wouldn't be able to decide which capture doesn't exist and this would result in failing to set #2. White mustn't try 2.Sed4# because of 1...Qd7!, so remains 2.Sbd4#, if impossible (1...Qb7), 2.Sed4# follows.

- "check on long diagonal" - question "Are there any?" is useless as answer is surely "No" because of check. White mustn't try 2.Sbd4# because of 1...Rf4!, so remains 2.Sed4#, if impossible (1...Rf2), 2.Sbd4# follows.

- if "capture on g6", 2.Sbd4# (white must recover f7!)

(The reason for g4 in key move is possibility 1...Kf5.)

Solution is given in standard formal Kriegspiel notation as it was submitted by competition winner Olivier Ronat.

1.Kd1!

2.Ke2 (illegal move) // (case 1...Kf1)

2.Rd2 Kg1 3.Ke1 Kh1 4.Kf2 Kh2 5.Rd3 Kh1 6.Rh3#

2.Ke2 (No announcement) (cases 1...Kg1 or 1...Kg2)

3.Kf2 (illegal move)//Kf3 (illegal move)// 3.Re3 (case 2...Kg2 from 1...Kg1)

4.Kf2 (illegal move)// 4.Kf3 (case 3...Kg1)

5.Kg3 (illegal move)// 5.Kf2 (case 4...Kh2) Kh1 6.Rh3#

5.Kg3 (No announcement) (case 4...Kh1 or 4...Kf1) Kg1 6.Re1#

4.Kf2 (No announcement) (cases 3...Kh1 or 3...Kh2)

5.Kg3 (illegal move)// 5.Rg3 (cases 3...Kh1 and 4...Kh2) Kh1 6.Rh3#

5.Kg3 (No announcement) (cases 3...Kh2 and 4...Kh1) Kg1 6.Re1#

3.Kf2 (illegal move)// 3.Kf3 (No announcement) (case 2...Kg1 from 1...Kg2)

4.Kf2 (illegal move)// (case 3...Kf1) 4.Rd1#

4.Kf2 (No announcement) (case 3...Kh2 or 3...Kh1)

5.Kg3 (illegal move) // 5.Rg3 (R‚3) Kh1 6.Rh3# (case 4...Kh2 from 3...Kh1)

5.Kg3 (No announcement) 5.Kg3 Kg1 6.Rd1# (case 4...Kh1 from 3...Kh2)

3.Kf2 (No announcement) (case 2...Kh1 or 2...Kh2 from 1...Kg1/Kg2)

4.Kg3 (illegal move)// (case 3...Kh2) 4.Rg3 (R‚3) Kh1 5.Rh3#

4.Kg3 (No announcement) (case 3...Kh1) Kg1 5.Rd1#

Comments to Juraj Lörinc.

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