A Kriegspiel Problem

Can a blind person listening to a game of kriegspiel be able to deduce a mate for one of the players?

Here is an attempt to answer this question in the affirmative. However, this requires a clarification of the definition of a ``No''. In the following problem, we use the most liberal definition of a ``No'' as an attempt by a player to make a move that appears legal only taking into consideration his pieces on his own board, but is in fact illegal according to the actual position as seen by the referee. Some players require, in addition, an attempted move by a player to be ``consistent with the current announcement''. In fact most players, and also the RAND rules, consider this stricter definition of a ``No'' to be in force if the present announcement is a check of some sort. Under this stricter definition, the number of ``Nos'' White receives in trying to make his 10th move must be decreased to, say 14.

Announcement Announcement
1. White. Black.
2. White. Black.
3. White. Black.
4. White. Black.
5. White. Try, d4.
6. Pawn gone, d4. Try, c3.
7. Piece gone, c3. Try there. Black.
8. Check long diagonal. Black.
9. Tries, d7 and f7 Try b5.
10. Tries, d7 and f7. No. No. ... No.
(16 or 17 Nos).

At which time, a person sitting in the next room listening to the game, shouts, ``White to mate in 3''.

T. S. Ferguson and J. B. MacQueen, 1976.

The announcements are made according to the RAND rules. For this problem, I hope the following explanation suffices.

(1) Pawn tries (i.e. possible pawn captures) are announced by specifying the square of the capture. Thus the announcement preceeding black's 5th move tells the players that black has a pawn that can make a capture by moving to d4.

(2) Captures are announced by specifying the square and whether a pawn or a piece was captured. Thus the announcement preceeding white's 6th move tells the players that white has lost a pawn that was on d4.

(3) Checks and the direction of the check (horizontal, vertical, one of the two diagonals or by a knight) are announced. Thus, the announcement preceeding white's 8th move tells the players that white is in check by a diagonally capturing piece (queen, bishop, or pawn) and that the check is along the longer of the two diagonals that meet at the square the white king occupies.

(4) There are two other types of `Nos`. There is the `Repeat No`, announced when a player tries a move that has already received a `No`, and there is the `Hell No`, announced when a player tries a move that is illegal on his own board.