Free logic puzzles to play and print

Matchstick Puzzles: Fix the Equation

The equation is wrong. Move, remove or add matchsticks to make it true.

Matchstick puzzles are equation puzzles built from matchsticks. The equation shown is false, and you make it true by moving, removing or adding sticks. This free matchstick equation puzzle tool runs in your browser, with no sign-up and nothing uploaded. You can play on screen or print puzzles with answers. Digits are drawn as seven-segment figures, so every number is made of sticks you can count. Puzzles come in Easy, Medium and Hard sizes, and each one has exactly one solution. Whether you want a matchstick math puzzle to solve yourself or a printed set of puzzles using matchsticks for a class, the tool covers both. Some people call these toothpick puzzles or match stick puzzles, and the idea is the same.

How to use the Matchstick Puzzles tool

  1. Pick a puzzle type from the chips: Move 1 stick, Move 2 sticks, Remove 1 stick, Remove 2 sticks, Add 1 stick or Add 2 sticks. The starting equation is always false.
  2. For a move puzzle, tap a stick to lift it.
  3. Tap a dashed empty place to put the stick down.
  4. For remove puzzles, tap a stick to take it away. For add puzzles, tap an empty place to add a stick.
  5. Watch the counter, which shows how many moves you have left. The equation is checked automatically as you go.
  6. If you are stuck, press Hint. There are two levels, so you can get a small nudge before the full answer.
  7. Press Check to test your answer. Press Show solution to see it. Moved sticks appear in green, and their old places are dashed red.
  8. Use Undo and Redo to step back and forward, or Reset to start the puzzle again. Press New puzzle for another one. Each puzzle has a number, and Copy link is there to share the one you are on.

To print, open the Print tab. Choose a puzzle type or Mixed (move, remove, add), then pick a difficulty. Set 4 to 8 puzzles per page and 1 to 10 pages, and choose Letter or A4 paper. Answer pages show moved sticks in grey with their old place dashed. Add a name and date line if you need one, then press Print / Save as PDF.

How do matchstick equation puzzles work?

Each digit is built from matchsticks in the seven-segment style. A 0 uses 6 sticks, a 1 uses 2, a 2 uses 5, a 3 uses 5, a 4 uses 4, a 5 uses 5, a 6 uses 6 (with the top bar), a 7 uses 3, an 8 uses 7 and a 9 uses 6 (with the bottom bar). The signs are built from sticks too: ‘-’ is 1, ‘+’ is 2 (one horizontal and one vertical), and ‘=’ is 2 horizontals. The ‘×’ sign uses 2 diagonals, and it only appears when the tool’s “Include the × sign” option is on.

Matchstick tricks: which moves are allowed?

A stick can move to another digit, to a sign, or inside its own digit. For example, a 6 can become a 9 by moving a stick within the same digit, and a ‘+’ can become an ‘=’. The number of digits never changes, so you cannot start a new digit. The result must be a true equation with exactly one ‘=’ sign. A two-digit number cannot start with a zero, and negative numbers are not allowed. The ‘=’ sign can end up somewhere else, so ‘5 - 3 = 2’ could become ‘5 = 3 + 2’. Moving the vertical stick off a ‘+’ turns it into a ‘-’.

Easy puzzles use one-digit numbers in the form a ± b = c. Medium puzzles have at least one two-digit number. Hard puzzles have three terms, such as a ± b ± c = d.

How do you solve move one matchstick puzzles?

Start by counting the sticks on each side of the equation, and look at the signs first, since ‘+’ and ‘-’ differ by one stick. Then look for a single stick that could change one digit or one sign, and check whether the new equation is true. Digits that differ by one stick are good places to look: 6, 8, 9 and 0; 3 and 9; 5, 6 and 9; 1 and 7. If the right side is too big to reach, try turning a ‘+’ into a ‘-’.

For example, ‘5 + 7 = 2’ becomes ‘9 - 7 = 2’. The vertical stick of the ‘+’ moves to the upper-right side of the 5, which turns it into a 9. A medium example is ‘74 - 9 = 6’, which becomes ‘14 - 8 = 6’. The top bar of the 7 moves onto the 9, turning the 7 into a 1 and the 9 into an 8.

Frequently asked questions

Can I print matchstick puzzles with answers as a PDF?

Yes. Open the Print tab, choose your puzzle type and difficulty, and press Print / Save as PDF. The answer pages are included in the printout, with moved sticks in grey and their old places dashed.

Is the matchstick puzzle tool free, and do I need an account?

The tool is free. You do not need to sign up or make an account to play or print puzzles. Nothing you do is uploaded.

Does it work on a phone or tablet?

The tool runs in a web browser, and its main controls are taps: tap to lift a stick, then tap a dashed place to put it down. It works the same in a phone or tablet browser as on a computer.

What is the difference between Move, Remove and Add puzzles?

Move puzzles keep the same number of sticks and ask you to relocate them. Remove puzzles ask you to take sticks away, and Add puzzles ask you to place new sticks on empty spaces. The Mixed option in the Print tab combines all three types.

Does every puzzle have an answer?

Yes. Every generated puzzle has exactly one solution, which the tool finds by checking every possible stick move.

Why can’t a Move 2 puzzle be solved with one stick?

Move 2 puzzles always need two sticks to be moved. The tool never generates a Move 2 puzzle that has a one-stick solution, so you should look for a combination of two moves.