Rectangle packing puzzle — Printable Materials & Rules

Prepare a complete physical puzzle

Print the board and tile sheet at the same scale, using one hundred percent rather than shrinking one page separately. The board is four squares wide and four squares high. The six pieces are two squares measuring two by two cells and four rectangles measuring two by one cells. They cover sixteen cells in total. Cut only the outer border of each labeled piece, not the internal grid lines. Keep the reference solution away from players. One player can solve it alone; a gathering of up to eight can form pairs with separate copies.

Define a legal arrangement

Place every piece flat inside the board. Edges follow grid lines; pieces cannot overlap, hang outside, stack, or leave holes. A piece can turn by a quarter turn, but cannot be folded or trimmed. Every cell must be covered once and every piece used once. Do not count an arrangement that simply looks full if the pieces overlap underneath. This version is a spatial packing puzzle, not a speed cutting contest. Give everyone the same printed dimensions and finish cutting before starting any optional timer.

Work through a small example

Put a two-by-two square in the upper-left corner and another in the upper-right corner. Together they cover the first two rows. Four two-by-one rectangles can now lie horizontally across the bottom two rows, two per row. That is one valid solution and proves this starter set is solvable; there may be other arrangements. Hide that example until the group asks for a hint or finishes. During play, partners can propose a position by row and column, then test it physically. Move a piece back out if it blocks a later placement.

Check the result and end the round

When a pair thinks it has solved the board, ask the other partner to point to all six labels and trace the outer boundary. Count the sixteen covered cells and check the empty space under any suspicious overlap. The puzzle ends when the placement is legal, or after the announced ten-minute attempt. Sharing a hint does not eliminate a player. If comparing teams, award one completion point rather than ranking their cutting speed. For another round remove the pieces and let the person who previously checked the layout place the first tile.

Make paper handling easier

The shapes use labels as well as outlines and do not rely on color. Mount them on thicker paper only if your printer accepts it, or have an adult prepare pieces before guests arrive. Larger copies are fine when board and tiles are enlarged by exactly the same percentage. Players who cannot comfortably handle small paper can direct a partner. The host sheet includes a labeled solution so you can verify the set without guessing. The web page supplies printable materials, not an automatic drag-and-drop solver; no account, uploaded image, or external puzzle download is required.

Count before handing out sets

Each pair should receive exactly one board, two square pieces, and four rectangular pieces. Count the labels A through F after cutting, since a missing rectangle makes the task impossible even though the board is correct. If paper edges curl, flatten the pieces before play. Do not use the blank space between printed shapes as an extra seventh piece.