Move exactly one match to make the equation true.
You may not remove matches, add new ones or leave a match lying loose.
💡 Hint
The left side is already right. Work out which digit the 3 must become, then compare the two shapes stick by stick and count how many differ.
Reveal answer
Move the lower-right match of the 3 to the lower-left position. The equation becomes 1 + 1 = 2.
Step-by-step solution
- Work out the target: 1 + 1 is 2, so the 3 must become a 2.
- Compare the shapes. A 3 uses the top, middle and bottom bars plus the upper-right and lower-right sticks.
- A 2 uses the same three bars plus the upper-right and lower-left sticks. The only difference is one vertical stick on the bottom half.
- Slide the lower-right stick of the 3 across to the lower-left. The 3 becomes a 2 and the equation reads 1 + 1 = 2.
- We checked every possible single move by computer. This is the only one that produces a true equation.
Why it fools people
It fools people because the error looks like it lives in the math, when it really lives in the drawing. Solvers stare at 1 + 1 and wonder what trick could make it equal 3, instead of asking which digit is easiest to rebuild. The 3 and the 2 also look very different at a glance, so it is surprising that they differ by just one stick that changes sides.
Did you get it?
About This Puzzle
Matchstick equations look like arithmetic, but they are really small building problems. Every digit is made of matches laid out like the numbers on an old digital clock or a pocket calculator, and the plus and equals signs are made of matches too. You are not allowed to erase anything or bring in new material. You can only pick up one match and set it down somewhere else. This one is the classic starting point: the math everyone knows by heart, written down wrong. It takes most people under a minute, but it teaches the single most useful habit in the whole genre: compare the shapes, not just the values.
How to Think About It
Start with what the correct equation would have to say. The left side is very hard to change with one match, so ask what the right side should read instead. Then picture the current digit and the target digit side by side, as if they were drawn on a clock face with seven possible bars. Mark which bars the two shapes share and which bars differ. If exactly one bar needs to disappear and exactly one bar needs to appear, you have found a single move. If the difference is bigger, look for a different target.
Common Traps
The first trap is reaching for the ones on the left. A 1 is only two matches, and almost anything you do to it produces a shape that is not a digit at all. The second trap is the plus sign. Pulling a match from it is a common trick in harder puzzles, so people try it here, but a minus would demand a total of 0, and no single match turns this right side into a zero. The third trap is forgetting that the match you lift has to land somewhere sensible.
Where This Puzzle Comes From
Puzzles built from loose matches have been a parlor and kitchen-table pastime for generations, because all you needed was a matchbox and a flat surface. The equation style borrows the seven-bar digits of digital clocks and calculators, which made every number a set of separate, movable parts. Today these puzzles are usually drawn rather than played with real matches, which is safer and easier to share.
Try This Variation
Same move, new spot. The equation reads 6 + 2 = 9. Move exactly one match to make it true. This time the answer side is already correct, so look somewhere else.
Show the answer to the variation
Move the lower-left stick of the 2 to the lower-right position. The 2 becomes a 3 and the equation reads 6 + 3 = 9. It is the main puzzle in reverse: the same single stick switches sides, but on the left of the equals sign. A computer check confirms it is the only solution.