A Kriegspiel Problem: Solution
SolutionJoseph DiMuro was the first to solve the problem. The problem was on the Chess Variant Pages since October 14, 1996; and Joseph's solution came in on March 3, 1997. This was an especially hard problem, and specific congratulations go to Joseph DiMuro for solving it.
Here is his solution:
I finally solved your kriegspiel problem, and boy does my head ache! :-)
Okay, here's the LONG solution...
All of White's pawns are still on the board. The pawns from a2, f2, and h2 are still on their home squares. The pawn on g3 must be from g2. What about the pawn on g4? It must be from e2; it made 2 captures to get to g4. That leaves b2, c2, and d2. The pawn on h6 can only be from d2; it made four captures. There is no way of knowing whether the pawn on f7 is from b2 and the pawn on g7 is from c2 or vice versa, but either way, they made 8 captures together. 2+4+8=14. The pawns necessarily made 14 captures, so Black is down to a king and maybe one other piece.
Now, what could that other piece (if there is one) be? It must be the pawn from a7, and here's why: all 16 White pieces are still on the board, so Black made no captures. Because of this, no Black pawn could have left its starting file unless it promoted. Now, the 14 pawn captures were all made on the c-f files. So the problem is the pawns from a7 and b7, which never left their files unless they promoted. The pawn from b7 could have (and must have) promoted (and got captured later), but the pawn on a7 never promoted. Why? It could only have promoted by marching straight down the a-file (no captures!) and the pawn on a2 is in the way. So the pawn from a7 could not have been captured by the pawns; they must have captured every other Black piece (except the King). Black is down to his king and maybe a pawn on the a-file.
So far, so good. Now, where could the Black King be? It is White's move, so Black is not in check (but a Black pawn could be standing in the way of a check). Because of this, the Black king can only be on five squares: e2, e5, e6, h3, and a6 (but if the king is on a6, there must be a pawn on a7).
White should first try to move rook to a4. If there is a pawn on a3, a4, or there is no pawn, this will work. If the ref says the move is illegal, try rook to a5. If this doesn't work, try rook to a6; then rook to a7. One of these will work. As a result of White's first move, White will have a rook somewhere from a4 to a7 and Black will be down to his king, since White will have captured the Black pawn if there was one. (The exception is if there was a Black pawn on a3. The important thing to note is that the pawn can't move if it's on a3, so Black's next move must be with the king.)
If the king was on a6, then White just captured a pawn on a7 with the rook. Black is forced to take the bishop on b6 with his king; so if that bishop is taken, White should move the rook on d1 to d6, mate.
If the king was on e2, then Black is forced to capture the rook on d1 with his king. If the rook on d1 is taken, White knows the king is there and moves queen to e1, mate.
If the king was on h3, the king must either capture the pawn on h2 or the pawn on g4. If the pawn on h2 is taken, White moves rook to h1, mate. If the pawn on g4 is taken, White moves bishop to g2, discovered check and mate.
If the king was on e6, the king must move to e5. If the king was on e5, the king must move to e6. These are the last possibilities, and they are the only ones where no capture is made. So if Black doesn't capture, White knows the the king is on e5 or e6. How does White checkmate in this case? Remember that White's first move was rook to a4, a5, a6, or a7. Here's what White does if Black doesn't capture:
1. If White first moved rook to a4, White now moves queen to d6, mate.
2. If White first moved rook to a5, White now moves knight to c7, mate.
3. If White first moved rook to a6, White now moves bishop to c7, mate.
4. If White first moved rook to a7, White now moves rook to e7, mate.
(Note: all these moves mate whether the Black king was on e5 or e6.)
There! That's all the possible squares for the Black king. Now to take some Tylenol... :)
Written by Joseph DiMuro and Hans Bodlaender.
WWW page created: March 3, 1997.