This Matchstick Equation Is Wrong. Move One Stick to Fix It

Matchstick puzzles are the single most commonly broken puzzle format online, and the reason is always the same: nobody checked.

The classic failure is a puzzle that claims to have one solution and actually has three, because the person who made it found one move that worked and stopped looking. The comments then fill with people who found a different valid answer and were told they were wrong.

How this one is guaranteed

Each digit here is a seven-segment shape, and every segment is one matchstick. The plus sign is two sticks; a minus sign is one. The equals sign is fixed and cannot be touched.

To generate the puzzle, the program takes an equation that is currently false and then tries every legal move: it removes each stick in turn from each position, places it in each empty segment position in each position, and checks two things. First, does every glyph still form a valid digit or operator? Second, is the resulting equation arithmetically true?

Every move that passes both checks is collected. If two different moves produce two different valid equations, the puzzle is thrown away and another one is generated. Only an equation with exactly one solution is published.

Rules, stated properly

• Move one stick only. Not two, and not “move one and rotate another”.
• The stick must come from somewhere and go somewhere. You cannot remove a stick and leave it out, and you cannot add one.
• Every digit must still be a digit afterwards.
• The equals sign stays as it is.

Those rules are what the solver enforces, so they are the rules the answer obeys.

Have a go, then open the reveal. It shows the corrected equation with the moved stick highlighted.