Move exactly two matches to make it true.
Both moves must be used, and no match may be removed, added or left lying loose.
💡 Hint
Treat the two moves as a budget. Decide what the sign must become, then ask which digit can take the freed match and which one can be fixed by sliding a match within itself.
Reveal answer
Move the plus sign’s vertical match onto the 5 to make a 6, then move one match inside the 2 to make a 3. The equation becomes 16 − 3 = 13.
Step-by-step solution
- With a plus sign the answer would need to be 18, which is out of reach in two moves. So the sign becomes a minus, freeing one match.
- Move 1: a 6 is a 5 with an extra lower-left stick. Place the freed match there, and 15 becomes 16.
- Now the left side is 16 − 3, which is 13, so the 12 must become 13.
- Move 2: a 2 has the lower-left stick and a 3 has the lower-right stick instead. Slide that one match across, and 12 becomes 13.
- The equation reads 16 − 3 = 13, true, using exactly two moves. A computer search found no one-move solution and exactly one two-move solution.
Why it fools people
It fools people because the puzzle offers a correct equation that is not a correct answer. Seeing 15 − 3 = 12 appear after a single change gives a strong feeling of success, and many solvers stop checking. But a move means lifting a match and putting it down, and that leftover match has nowhere to go. The real solution adjusts both sides together, so the difference stays at 3 while both numbers shift up by one.
Did you get it?
About This Puzzle
This is where matchstick equations get serious. You must move exactly two matches, not one and not three, and the equation has to be true when you are done. Two moves sound like only twice the work, but the number of possibilities grows much faster than that, and the puzzle also contains a very convincing false finish. The digits are built in the seven-bar style of a digital clock, the plus sign is two crossing matches and every match on the table can be used. There is exactly one correct arrangement. Finding it requires respecting every rule, especially the one you will be tempted to bend.
How to Think About It
Treat the two moves as a budget. Changing the plus sign to a minus costs half a move: it frees one match that still has to be placed. Ask where that match can go so that the result is a valid digit. Then you have one full move left, which means lifting one match and placing it somewhere, possibly inside the same digit. After the first change, recompute what the subtraction needs, and look for a single rearrangement that restores balance. Check the final count: two lifts, two placements.
Common Traps
The big trap is noticing that 15 − 3 = 12 is already true once the sign changes. It feels like the answer, but it uses only one match, and that match would be left lying on the table, which breaks the rules. The second trap is keeping the plus sign and hunting for 18 on the right, which takes far more than two moves. A third is placing the spare match on a 1, which never yields a valid digit.
Where This Puzzle Comes From
Multi-move matchstick puzzles extend the classic single-move format found in puzzle books and newspaper columns. The “two moves exactly” rule is a common way to raise difficulty, since it rules out shortcuts and forces solvers to account for every match. Designers often build in a near-solution, like the one here, because a convincing false finish is what separates a hard puzzle from a merely long one.
Try This Variation
Now the false finish from the main puzzle becomes the target. The equation reads 14 + 3 = 12. Move exactly two matches to make it true. As before, both moves must be used and no match may be left lying loose.
Show the answer to the variation
Move the plus sign’s vertical match to the top of the 4, then move the 4’s upper-right stick to its bottom. The 4 becomes a 5 and the equation reads 15 − 3 = 12. A 4 and a 5 share only the middle bar, upper-left and lower-right sticks, so it takes both moves. A computer check confirms the solution is unique.