Matchstick Puzzle Solver
How to use the matchstick puzzle solver
Type the equation as it is made of matches, using + − × and =, then choose whether the puzzle asks you to move, take away or add matches, and how many. Show the answers draws every answer in matches: the blue ones are the matches put down, and the dashed outlines show where the moved ones came from. It tries every possibility, so when it says there is no answer, there is none.
Digits are the usual matchstick shapes: 6 has its top bar and 9 its bottom bar, 7 is three matches and 1 is two. A plus is two matches, and taking its upright away leaves a minus; laying a match next to a minus makes an equals sign. Those three swaps are behind half the puzzles in any book.
Matchstick puzzles with answers
Give me a puzzle makes a new one: it takes a true sum, moves one or two matches to break it, and keeps it only if it has exactly one answer, so there is no arguing about the solution. Try it, then press Show the answer. A few classics to type in yourself: 6 + 4 = 4 (move one, two answers), 5 + 7 = 2 (move one), and 3 + 3 = 5 (add one).
How to solve matchstick puzzles
Most answers come from a handful of digits that are one match apart. Learn this table and you will see the moves before you try them. It comes straight from the shapes above.
| Digit | Matches | Add one to make | Take one away to make | Move one inside it to make |
|---|---|---|---|---|
| 0 | 6 | 8 | – | 6, 9 |
| 1 | 2 | 7 | – | – |
| 2 | 5 | – | – | 3 |
| 3 | 5 | 9 | – | 2, 5 |
| 4 | 4 | – | – | – |
| 5 | 5 | 6, 9 | – | 3 |
| 6 | 6 | 8 | 5 | 0, 9 |
| 7 | 3 | – | 1 | – |
| 8 | 7 | – | 0, 6, 9 | – |
| 9 | 6 | 8 | 3, 5 | 0, 6 |
Then look at the operators: a plus can lend its upright, a minus can borrow a match to become an equals sign, and an equation can end up with its = in a different place. When one side is far too big, look for a digit that can lose a match, like 8 to 0, 6 or 9, or 9 to 3 or 5.
More brain teasers
If you like a puzzle where everything is in front of you and the answer is a matter of seeing it, the cryptarithm solver does the same for letter sums like SEND + MORE = MONEY. In wood and metal, our brain teasers work the same way: every piece in your hands, and one arrangement that works. There are more solvers on the puzzle tools page.
Frequently Asked Questions
What is the answer to 6 + 4 = 4 matchstick puzzle?
Move one match: take the middle bar of the 6 and put it in the top right, making 0 + 4 = 4. Or take the upright out of the plus to finish the 6 as an 8, making 8 - 4 = 4.
How do you solve matchstick puzzles?
Learn which digits are one match apart: 0, 6 and 9 turn into each other by moving one match, 3 into 2 or 5, and adding a match turns 1 into 7, 3 into 9, 5 into 6 or 9, and 0, 6 or 9 into 8. Then remember a plus can lend its upright to become a minus, and a minus can borrow one to become an equals sign.
How many matches make each digit?
1 takes two, 7 takes three, 4 takes four, 2, 3 and 5 take five, 0, 6 and 9 take six, and 8 takes seven, in the usual matchstick shapes.
What is the answer to 5 + 7 = 2?
Move one match from the plus sign to the 5, turning it into a 9: 9 - 7 = 2.
Can a matchstick puzzle have more than one answer?
Yes, many do, which is why the solver lists every answer. The puzzles it makes itself are checked to have exactly one.