Spatial planning
Block puzzles: plan for the shape you still need to place
Work through a coordinate-based board where two legal placements have very different consequences for the next piece.
A constructed placement puzzle with no row clearing, rotation, or random draws. The example isolates spatial fit rather than claiming a universal game strategy.
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Describe empty space by its shape
Six empty cells do not necessarily fit a six-cell piece. The cells must have the right adjacency and orientation. A useful scan therefore records empty rectangles, narrow corridors, and isolated holes, rather than only the number of unoccupied squares.
Our example uses a four-by-four board. Rows run from top to bottom, columns from left to right, and coordinates use (row, column). A dot is empty and # is occupied. Pieces cannot rotate, lines do not clear, and the next two pieces are a horizontal bar of length three followed by a two-by-two square. These deliberately limited rules make the outcome easy to reproduce.
c1 c2 c3 c4 r1 . . . # r2 # # # # r3 . . . . r4 . . . .
A legal bar placement can destroy every square placement
Place the bar at (3,1), (3,2), and (3,3). This is legal because those three cells are empty. However, only column 4 remains open in row 3, so no pair of adjacent empty columns spans rows 3 and 4. The square cannot fit there.
It cannot fit across rows 1 and 2 or across rows 2 and 3 either, because row 2 is fully occupied. Although eight empty cells remain after placing the bar, none form a two-by-two area. This is a concrete counterexample to choosing moves by empty-cell count alone.
Preserve the only region that supports the square
Instead place the bar in row 1 at columns 1 through 3. The lower two rows remain empty. The square then fits at rows 3 and 4, columns 1 and 2, or in either of the two other adjacent column pairs.
The first move is valuable because the top corridor serves the bar while the lower region serves both pieces. Use the specialized region for the piece that fits it, preserving the flexible region for the piece with fewer alternatives. This is a property of this board, not a guarantee that edge placement always wins.
After the bar: After the square: B B B # B B B # # # # # # # # # . . . . S S . . . . . . S S . .
Turn the example into a repeatable scan
When all upcoming pieces are visible, start with the hardest piece to accommodate. Count its legal placements. If a large square has only one available region, test whether the other pieces can avoid it. A small bar with several possible homes usually offers more flexibility.
After considering a placement, inspect what remains rather than admiring how neatly the placed piece touches an edge. A tidy-looking move can create single-cell holes. Conversely, a move in the center can be necessary to preserve a long corridor. Geometry, not visual tidiness, determines feasibility.
- Identify the footprint of every visible piece.
- Mark regions that can host the most constrained piece.
- Simulate the first placement and recount options for the remaining pieces.
- Recheck after any line clear; the geometry has changed.
Why line-clearing variants need a second calculation
In a game that clears completed rows immediately, our top bar would fill row 1 and could remove it. A lower placement might complete a column and open a route for the square. You must apply the clearing rule between moves before deciding the next piece is blocked.
Rotation also changes the options: a vertical bar could use a different corridor. Random future draws add uncertainty, so preserving a range of useful spaces becomes more reasonable than optimizing for an unseen exact shape. Our example teaches a question you can verify on your own board: which future placement disappears if I use these cells now?
