Matchstick Equation Puzzles
Each puzzle is a false equation drawn in sticks, like 6 + 4 = 4. Move one stick (or two) to make it true: 6 + 4 = 4 becomes 0 + 4 = 4 if the 6's middle stick moves to its upper right, or 8 − 4 = 4 if the plus gives its upright to the 6. Every digit has one fixed drawing, written out below, and every possible move is tried, so the page knows every answer each puzzle has. Choose puzzles with exactly one answer or allow several, check your answers here, and print a sheet with the answers on their own page.
What this generator does
Draws each digit with up to seven sticks in fixed places, a plus as two crossed sticks and a minus as one. It picks a false equation A + B = C or A − B = C, then lifts every possible stick, or pair of sticks, and puts it into every empty place, keeping only results where every symbol is still a digit or sign and the sum is true. A puzzle is kept when there is at least one answer (exactly one, if you ask for that), and for two sticks only when moving one stick cannot solve it.
How to use this tool
- Choose how many sticks to move and whether each puzzle must have exactly one answer.
- Press Make the puzzles. Type an answer such as 8 − 4 = 4 and press Check; a hyphen counts as minus.
- Open Every answer to see each one with the moved sticks marked, or print the puzzles and the answers.
Understanding the controls
- Sticks to move
- One or two. Two-stick puzzles are chosen so that no single move works.
- Answers
- Exactly one: each puzzle has a single answer under these rules. One or more: some puzzles have several, and the key lists them all.
- Seed
- Optional. The same seed and settings make the same six puzzles while the generator is unchanged.
Worked examples
- 6 + 4 = 4, move one stick
- Two answers: 0 + 4 = 4 (the 6's middle stick moves to its upper right) and 8 − 4 = 4 (the plus's upright completes the 8).
- 15 + 19 = 2, move two sticks
- One answer: 75 − 73 = 2. The plus gives its upright and the 9 its upper left stick; both 1s gain a top stick and become 7s.
Common use cases
- A short starter for a maths lesson, with every answer known in advance
- A puzzle sheet where some equations have more than one answer, for a class to find them all
- Two-stick puzzles that cannot be done with one, for readers who found one stick too easy
How this generator works
Digits are drawn as on a seven-part display: 0 uses six sticks, 1 the two on the right, 7 three (top and right), 6 and 9 six each with the top and bottom sticks kept, and 8 all seven. A shape that is none of these is not a digit. The equals sign never changes, the number of digits never changes, and no number may start with 0. The search tries every way to take k sticks and put them in k empty places, which is at most a few hundred thousand cases. Every answer is then checked again by a separate routine that compares the two equations stick by stick, using its own written-out table of shapes, and redoes the arithmetic.
Randomness and fairness
Numbers come from the browser's secure generator, or a seeded one when you type a seed. Seeds are deterministic, not cryptographic, and not a secret. The answers are not random: they come from trying every move.
For how randomness is produced across the whole site, see how Generate Random works.
Assumptions this tool makes
- Sticks are moved, never added or removed, and a moved stick may be turned to fit its new place.
Limitations and good to know
- Exactly one answer is under these rules and drawings only; with other digit shapes, or moves such as turning the equals sign, a puzzle may have more.
- Numbers have one or two digits and sums use only plus and minus.
- Two sticks means a larger search, not a measured difficulty.
Common mistakes
- Turning the equals sign into a minus or a plus
- The equals sign is fixed here; only digits and the plus or minus change.
- Drawing 7 with four sticks or 9 without its bottom stick
- Each digit has one drawing here; compare with the shapes on the page.
Privacy and your data
Puzzles are made in your browser. With analytics consent, a count records that puzzles were made or checked; your answers are not sent.
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