The Floating Square: Two Passed Pawns Against a King
Black to play and win
PlayTwo of your passed pawns stand on the same rank, a5 and e5. Build the square that has them as corners. It reaches the edge of the board, and that means one of them queens whatever the king does.
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The Floating Square: When One Pawn Must Queen
Black to play and win · Win against perfect defense
Waking the engine…
The theory
Watch the method: press play to see the winning idea run, or step through it move by move.
The floating-square rule (Studenecki, 1939): take two passed pawns on the same rank and build the square that has them as adjacent corners. Here a5 and e5 give a5-e5-e1-a1, which reaches the first rank. A single king cannot stop both. Meanwhile your own king on g7 holds White's g6 and h5 pawns, and it must stay there: Kf8, Kg8 and Kh8 all lose.
The rule of the square handles one pawn. For two separated passed pawns standing on the same rank, use the floating square.
The rule (Studenecki, 1939). Build the square that has the two pawns as adjacent corners. If it reaches the edge of the board, one of the pawns must queen, whoever is to move. If it stops short of the edge, the king holds them.
Here it reaches. a5 and e5 give the square a5-e5-e1-a1, and a1 is on the edge. The white king cannot cover both files.
Your king has a job too. It stays on g7 to blockade White's g6 and h5 pawns. Wander off with Kf8, Kg8 or Kh8 and you lose the game instead of winning it.
In this drill the defense never cracks. Play a4, then the only move e4, and one pawn goes through.
Keep going
The Floating Square That Falls Short
Black to play and draw
Two Files Apart: The King Wins Both Pawns
White to play and win
Three Connected Pawns and the One Square That Wins
White to play and win
All 68 king & pawn positionsFollow the full curriculum (free)