Move exactly one match to make it true.
You may not remove matches or add new ones.
💡 Hint
Changing the 5 costs too many matches. Look at the plus sign and the 3 together, and ask what each could gain or lose.
Reveal answer
Take the vertical match from the plus sign and use it to turn the 3 into a 9. The equation becomes 9 − 4 = 5.
Step-by-step solution
- With a plus sign the answer would need to be 7, and no single move turns this 5 into a 7. So try a minus.
- Lifting the vertical match out of the plus sign leaves a minus sign and gives you one spare match.
- For a subtraction ending in 4 = 5, the first number must be 9.
- A 3 has the top, middle and bottom bars plus both right-hand sticks. A 9 has all of those plus the upper-left stick. Place the spare match there.
- The equation now reads 9 − 4 = 5, which is true. A computer search of every single move found no other solution.
Why it fools people
The puzzle works because our attention goes straight to the answer. When a sum is wrong, we assume the total is the problem, and a gap of two feels small and fixable. But in a matchstick puzzle, numerical distance means nothing; what counts is how many sticks two shapes share. The real move happens on the far left, in a digit nobody suspected, using a match borrowed from a symbol.
Did you get it?
About This Puzzle
At first glance, 3 + 4 = 5 looks like the easiest repair job in the world: the answer is off by two, so surely the 5 just needs a little work. That instinct is exactly what this puzzle is built to catch. The digits are drawn with matches in the familiar seven-bar style of a digital clock, and the plus sign is made of two matches as well. Every match on the table is fair game, including the ones that are not part of a number. Look at the whole equation, symbols included, before you decide which match is going to move.
How to Think About It
List the ways the equation could become true and test each one for cost. If the sign stays a plus, the answer must be 7, so ask how many matches separate a 5 from a 7. If the sign becomes a minus, the plus gives up one match, and that match must be placed somewhere. Then ask which first number would make the subtraction work, and whether the 3 can become that number by gaining exactly one stick. A move that costs nothing extra is the one you want.
Common Traps
The tempting fix is to turn the 5 into a 7. It feels close because the answer is off by only two, but a 5 and a 7 share just two bars, so the change takes several moves. A second trap is trying to make the 4 smaller so that 3 plus something equals 5. A 4 can become a few shapes, but none of them gives 2. The last trap is treating the plus sign as fixed scenery, which hides the spare match.
Where This Puzzle Comes From
Borrowing a match from the operator is one of the oldest tricks in matchstick equations, and once you know it you will check plus signs first. These puzzles belong to the broader family of stick and toothpick puzzles that have filled puzzle books and newspaper corners for decades. Equations became especially popular once digital displays made the seven-bar digit shape familiar to everyone.
Try This Variation
Try the same trick on a new equation: 5 + 7 = 2. Move exactly one match to make it true. Remember that the first number can grow if the sign gives something up.
Show the answer to the variation
Take the vertical match from the plus sign and add it to the 5 as its upper-right stick, turning the 5 into a 9. The equation becomes 9 − 7 = 2, which is true. A computer check confirms that no other single move works.