# Gravity Chess - Slipping Through the Cracks

Chess Mate Attack is a mobile puzzle game released earlier this year. Each of its 90 (at time of writing) levels follows the same basic principles:

• Play takes place on an $$m×n$$ chessboard, whose squares are either empty or occupied by pieces (red or blue), walls, or floors.
• You control whichever blue pieces are present, and move them as in chess, with the caveat that after every move, pieces fall until they are blocked by a wall, a floor, or a piece of the same color. If a piece lands in a space occupied by a piece of a different color, the opposing piece is captured and removed from play. (Opposing pieces may also be captured in the "normal" fashion.)
• Walls can be jumped over by knights, and floors can be passed through in any direction by any piece but cannot be fallen through. (Neither of these facts are relevant to this puzzle.)
• The goal is to capture the red King.

Consider the following board, taken from the game, where yellow boxes are walls and the two pieces are the red King and blue Queen:
In the original game, the red King remains stationary, and can be captured on the fourth move. However, if the red King moves after each of your moves (subject to gravity, just like you), capturing takes seven moves. Can you find the best strategies for both players?

• you should have said that the blue piece is a queen :))
– daw
Jul 12 at 16:01
• That would be implied by the move indicators, but I'll add it for completeness :^) Jul 12 at 16:05
• What does "mate" mean when the king does not move? I can attack the king in three moves, and take it on the fourth, but "normal" chess does not count the move required to capture the king in "mate in N" puzzles.
– fljx
Jul 12 at 16:17
• and by "mate in four" you mean "king is taken with the fourth move", right? (because I can place the unmoving king in an inescapable check with three moves.)
– Bass
Jul 12 at 16:19
• @justhalf Well, this question is tagged chess, and the queen moves "as in chess". Apart from gravity, the king doesn't have any special movement rules given here, so the only thing that keeps it from teleporting around the board is the implication that it, too, moves as in chess. In chess, pursuant to FIDE rule 3.9.2, it is illegal for the king to move into a threatened square. In the best-for-both sequence this would lead into a stalemate. Also, please don't spam.
– Bass
Jul 13 at 7:27

Assuming stalemates don't exist in this game, here's a way to catch the king in 7 moves.

I'm using normal chess board coordinates so that the top left is a8.

 1. Qe2      Kc8->c7 (Blue has only 1 way up. Red can pass for the 1st move.)
2. Qf2      Kd8->d6 (d6 has the best escape route for the King.)
3. Qg3+     Kc5->c4 (Kick the King off the top stairs)
4. Qf2+     Kb3->b2 (f2 is the quickest way back. King has only one way to avoid capture)
5. Qc5->c4+ Kc2
6. Qc5->c4  Kb2     (Blue "passes", creating a stalemate! Red has to move into a threatened square.)
7. Qb3->xb2#


(If the stalemate rule exists, then the king is safe at c2, as the queen cannot enter the bottom left without getting trapped in there.)

• Move 4-6 are not checks, right? f2 doesn't check c4 Jul 13 at 2:54
• @justhalf They are. (Except move 6, sorry about that, fixed now.) Blue's move 5 is literally queen from f2 to c4.
– Bass
Jul 13 at 7:30
• Huh? After Kc5->c4, red king is at c4, then with 4. Qf2, it is not a check since f2 doesn't attack c4? Are you considering that the King is still at c5? Why? Jul 13 at 19:28
• Ohh, you are considering the drop-move as threatened as well. Now everything makes sense, including the stalemate claim. Jul 13 at 19:31