Tarsia Puzzle Generator

What this generator does

Cuts a set of question-and-answer pairs into triangles whose edges carry one half of a pair each, shuffles and turns them for cutting out, and checks that every touching edge is a matched pair and nothing is written twice, so the pieces fit back together only one way.

How to use this tool

1. Choose what the pairs are — one of the arithmetic kinds, or your own pairs typed in.
2. Choose how big the triangle is, from four pieces up to twenty-five.
3. Decide whether the outside edges carry questions too. Leaving them blank makes the border easy to spot.
4. Make the puzzle, print the pieces, and cut them out.
5. Show the answer for the finished shape, or give a seed to print the same puzzle for another class.

Understanding the controls

What the pairs are

Ten kinds of arithmetic, or your own pairs typed one per line with an equals sign between them. Your pairs are printed exactly as given.

How big the triangle is

A side of two is four pieces and three pairs to match; a side of five is twenty-five pieces and thirty pairs, which is a lesson rather than a starter. With questions on the outside edges it needs three more pairs per side — 9, 18, 30 and 45 in all — and the gentle division, number-bond and place-value questions do not have that many different answers, so the larger sizes are refused for them.

How hard

Passed to the arithmetic, so a stretch addition really is a harder sum rather than the same sum printed smaller.

Questions on the outside edges

With them off, the border of the finished shape is the edges with nothing on them, which gives most of the puzzle away. With them on, the border has to be worked out.

Seed

A word gives back the same puzzle, including which pieces were turned and how far, for as long as the generator is unchanged.

Common use cases

• A starter that a table can do together without a teacher marking it
• Practice that tells a pupil they are wrong before an adult does
• Revision of a topic where the pairs are already written down
• A cover lesson with an answer sheet that takes a glance
• Vocabulary or definitions matched up, using your own pairs

Randomness and fairness

Which pairs are drawn, which half of a pair goes on which piece, and how far each piece is turned before printing are all decided using the browser's secure generator. Typing a seed switches to a repeatable sequence instead, so the same puzzle can be printed twice; that path is for reproducibility and is not cryptographically strong.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

• Every question and every answer in one puzzle has to be different. A pair that repeats a question or an answer already used is left out, and if that leaves too few pairs the puzzle is refused, because a repeated pair would let a piece sit in two places. Different means different as written: in a rounding puzzle 17.0 and 17.00 are two answers, as they are to whoever marks it.
• The finished shape can be turned a third of a turn either way and still be right, so an answer sheet held at a different angle to a pupil's table is the same answer.
• Twenty-five pieces is the most. Beyond that the triangles are too small to read once they have been cut out.
• Your own pairs are printed as typed. Nothing here checks that an answer is the right answer to its question.

Privacy and your data

The puzzle is built in your browser. Pairs you type are never transmitted or stored; the site's counters record that a puzzle was made and how many pieces it has.