Block Fit — Place Shapes to Fill the Grid
Place every shape on the board to fill all cells. No gravity, no overlaps — pure packing logic.
How to play
- Click a shape in the tray to select it — it gets a yellow highlight.
- Click a board cell to drop the shape with its top-left corner there.
- Shapes can't overlap each other or extend past the board edge.
- Fill all 25 cells to solve; click 'New Puzzle' to reset the board.
You have a tray of polyomino shapes and an empty board. Select a shape, then click the board cell where its top-left corner should go. Shapes cannot overlap or hang off the edge. Fill every cell to win — no gravity, just pure spatial packing.
How it works
Block Fit is a spatial packing puzzle. You are given a set of polyomino shapes — pieces made of connected squares — and a grid with empty cells. Your task is to place every piece onto the grid so that together they cover every cell exactly once, with no overlaps and no pieces hanging off the board.
This type of puzzle is related to exact cover problems in combinatorics, the same family that Sudoku, Tetris, and pentomino tiling belong to. Unlike Tetris there is no gravity, and pieces may not be rotatable depending on the puzzle; you place them where they fit.
An effective strategy is to start with the largest or most irregular pieces first, since they have the fewest valid placements. Smaller, square pieces are more flexible and easier to fit around larger constraints. Eliminating impossible positions for an awkward L-shaped or S-shaped piece early dramatically reduces the search space.
Block Fit exercises visual-spatial reasoning, forward planning, and pattern recognition, making it popular in puzzle collections and educational settings for developing geometric thinking.
Worked example
Place a 5-piece set on a 4x4 grid
- Start with the largest piece (e.g., an L-shaped 4-cell piece). Try each corner of the grid.
- Place the L in the top-left corner — it leaves an irregular remaining region.
- Take the next most constrained piece and fit it into the tightest remaining gap.
- Continue placing pieces from most constrained to least constrained.
- The last small square piece fills the final empty cell.
All pieces placed with no gaps or overlaps.
Common mistakes to avoid
- Placing small, flexible pieces first and then getting stuck with an irregular large piece that no longer fits the remaining space.
- Not considering that a piece might need to be placed in a counter-intuitive orientation to allow later pieces to fit.
- Giving up too quickly after the first failed arrangement — systematic backtracking is normal and expected in packing puzzles.
Key terms
- Polyomino
- A plane figure made by joining unit squares edge-to-edge; tetrominos (4 squares) and pentominos (5 squares) are common examples.
- Exact cover
- A solution where every cell is covered by exactly one piece — no gaps and no overlaps.
- Packing puzzle
- A class of puzzle where the challenge is fitting all pieces into a confined space without overlaps.
Frequently asked questions
- How do I place a shape?
- Click a shape in the tray to select it (it highlights), then click the board cell where the shape's top-left corner should land.
- What if a shape doesn't fit?
- Nothing is placed and you'll see a hint. Pick a different cell or a different shape.