Pattern Block Puzzle Generator
Grows an original silhouette from pattern blocks laid edge to edge and prints its outline at the size of your blocks, with the exact pieces to use: so many hexagons, trapezoids, rhombuses and triangles. Pupils fill it with real blocks. The answer page shows one way to do it, and the page counts every way the listed pieces can fill the outline, so it can say whether the answer is the only one — or ask for silhouettes that have just one.
What this generator does
Gives pattern-block puzzles that fit real blocks, with a stated piece list and an exact statement of how many answers there are, rather than a picture with one answer and no way to know if another is also right.
How to use this tool
- Choose the size in triangle units, the kind of pieces and how many silhouettes.
- Measure an edge of one of your blocks and enter it (25.4 mm suits many sets).
- Tick 'Only silhouettes with a single way to fill them' for a puzzle with one answer.
- Press Make silhouettes, then print at 100% scale: one silhouette per page, with a bar to check the size, and an answers page.
Understanding the controls
- Size
- 6 to 36 triangle units: a hexagon is 6, a trapezoid 3, a rhombus 2, a triangle 1.
- Pieces
- A mix of all four, mostly big pieces, or no hexagons (more ways to fill, so harder to be sure).
- Block edge on paper
- The edge length the silhouettes print at; measure your own blocks. A bar of that length is printed to check the scale.
- Single answer
- Keeps only silhouettes the search fills in exactly one way.
- Paper and seed
- Paper size for printing; a seed rebuilds the same silhouettes while the generator is unchanged.
Worked examples
- Seed 'hive', 24 units, a mix, two silhouettes
- Silhouette 1 uses 3 hexagons, 1 trapezoid, 1 rhombus and 1 triangle, and the search finds only one way to fill it. Silhouette 2 uses 2 hexagons, 5 rhombuses and 2 triangles, also with a single answer.
Common use cases
- Pattern-block mats for early geometry and fractions of a hexagon
- Problem-solving: is there another way to fill it?
- A quiet table activity with real blocks
How this generator works
The four pieces used here are made of one equilateral triangle size, so a silhouette is a set of triangles on a fixed grid. Pieces are added edge to edge at the border until the size is reached. A search then fills the outline in every possible way with exactly the listed pieces, stopping at 200 or after a fixed amount of work and then saying 'at least'. Each answer is replayed before display: every piece has its true shape, none overlap, and together they cover the outline exactly.
Randomness and fairness
Pieces and positions are drawn with the browser's cryptographically secure generator, or from one seeded draw when a seed is typed. Seeded sheets are deterministic, not cryptographic. The answer count is computed by search.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Only the hexagon, trapezoid, wide rhombus and triangle are used. Squares and thin rhombuses do not sit on the same triangle grid, so they are left out.
- Silhouettes print at the edge length you give; if your printer scales the page, the bar on the sheet will not match a block edge.
- The colours named (yellow hexagon, red trapezoid, blue rhombus, green triangle) are those of many sets, not all; the drawings are in greys.
Related generators
- Length Rod Challenge GeneratorPrintable number-rod challenges: make a train of rods as long as a target, with the exact number of trains or sets of rods that work, counted by the generator.
- Tessellation GeneratorTiles a grid with squares, offset bricks or dominoes, checking cell by cell that nothing is uncovered and nothing is covered twice.
- Fractions Worksheet GeneratorSheets on adding, multiplying, simplifying and comparing fractions, with every answer given in its simplest form and checked.
- Lattice Polygon GeneratorPolygons with every corner on the integer grid, where the area is worked out twice — by the shoelace formula and by counting points — and the two agree.