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Tarsia Puzzle Generator

A matching jigsaw marks itself. The triangles only go together when every edge that ends up touching another has a question on one side and that question's answer on the other, so a pair that has been got wrong shows up as a shape that will not close. That is a claim worth proving rather than asserting, and it is proved here by laying every piece in every place in every turn: exactly three arrangements close, and they are the same finished triangle turned a third and two thirds of the way round.

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 proves the pieces fit back together in only one arrangement.

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.
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 exactly the same puzzle, including which pieces were turned and how far.

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 set of pairs with repeats in it is refused rather than used, because a repeated pair would let a piece sit in two places.
  • 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, and nothing about them reaches the site's counters.