Move exactly one match to make it true.
You may not remove matches or add new ones.
💡 Hint
Think about what kind of equation naturally ends at zero. Then compare the 1 with the 7, and ask where one spare match could come from.
Reveal answer
Take the vertical match out of the plus sign and lay it across the top of the 1 to make a 7. The equation becomes 7 − 7 = 0.
Step-by-step solution
- Zero is easiest to reach by subtraction: any number minus itself is 0.
- A 7 is made of three matches: a top bar and the two right-hand sticks. A 1 is just the two right-hand sticks. So a 1 becomes a 7 by gaining a top bar.
- Lift the vertical match out of the plus sign. The plus becomes a minus and you have one spare match.
- Lay the spare match across the top of the 1. The equation now reads 7 − 7 = 0, which is true.
- A full computer search of single moves found no other solution.
Why it fools people
It fools people because zero feels like a dead end. We think of it as nothing, so we look for ways to make nothing appear, instead of building two equal quantities that cancel out. The puzzle also hides its solution in a double change. Solvers who find one half, either the minus sign or the new 7, often stop there because the other half is not yet visible.
Did you get it?
About This Puzzle
Two positive numbers can never add up to zero, so this equation looks hopeless the moment you read it. That is what makes it a good medium puzzle. A single match has to do two jobs at once: it has to change the operation and change a number, and both changes have to land together. The digits are built in the seven-bar style of a digital clock, and the plus sign is two matches crossing. If you have solved a few easy matchstick equations, you already own every tool you need. The challenge is seeing which result is easiest to build when the target is zero.
How to Think About It
Begin with the answer side and ask what kinds of equations naturally end in zero. With addition, both numbers would have to be zero, which is far away. With subtraction, you only need two equal numbers. So the question becomes: can the left side turn into a number minus itself with one move? Count the matches in each digit. Then think about where a spare match could come from, and where it could go, so that one lift and one placement achieve both changes at once.
Common Traps
Many people try to change the 0 instead, turning it into an 8 by adding a middle bar. That gives 7 + 1 = 8, which is correct, but the match has to come from somewhere, and taking it from the 7 or the 1 breaks those digits. Others try to turn the 7 into a 1 to get 1 − 1 = 0, but that removes a match and leaves it with nowhere legal to go. A third trap is assuming zero is impossible and quitting early.
Where This Puzzle Comes From
Puzzles that ask you to make an equation true by moving sticks are a long-standing staple of puzzle books and brain-teaser collections. This one belongs to the family of operator-swap equations, where the plus sign gives up a match to become a minus. Designers like zero targets because the “number minus itself” idea is simple once seen, yet rarely the first thing people try.
Try This Variation
Another zero, a different fix. The equation reads 9 + 1 = 0. Move exactly one match to make it true. This time the 1 cannot become a 9 in one move, so look elsewhere.
Show the answer to the variation
Take the vertical match from the plus sign and lay it across the middle of the 0, turning it into an 8. The equation becomes 9 − 1 = 8. The same spare match is used, but here it builds the answer instead of a matching number. A computer check confirms it is the only solution.