Puzzle E1 (easy)
Move exactly one match to make the equation true.
Tap a match to pick it up. Dashed spots show where it can go, and the board tells you right away if the new equation is true. Hint goes in three steps: first it names the number or sign the match comes from, then it highlights the match, then it shows where it goes. With a keyboard, Tab to a match and press Enter, then Tab to a spot and press Enter again. Your solved puzzles are remembered in this browser, so you can come back later and carry on.
The rules
People argue about matchstick puzzles mostly because nobody says the rules out loud. Here they are, and the board above follows them exactly:
- Move exactly one match. You can't add one, throw one away, break one or lay one diagonally.
- Digits are drawn like a digital clock, with seven possible matches each. A 1 is two upright matches, and it may stand on either side of its space.
- Signs are made of matches too. A minus is one match, a plus is two (one flat, one upright) and an equals sign is two flat matches. So a sign can change into another sign.
- The result has to be a real equation: numbers and plus or minus signs, exactly one equals sign, and both sides equal. No numbers that start with a zero, like 05, and no sign at the very start.
Every puzzle on this page leads to exactly one true equation under those rules. I checked each one with a program that tries every possible move, so if you find a second answer, I'd honestly like to hear about it. The board accepts any true equation you make, not just the one in the answer key.
How to solve them
Here's the trick most people never notice: there are only a few ways a digit can change with one match. The table uses the usual 1 on the right side of its space. If you know them, you stop staring at the whole equation and start checking a short list.
| Digit | Matches | Move one of its own | Take one away | Add one |
|---|---|---|---|---|
| 0 | 6 | 6, 9 | nothing | 8 |
| 1 | 2 | nothing | nothing | 7 |
| 2 | 5 | 3 | nothing | nothing |
| 3 | 5 | 2, 5 | nothing | 9 |
| 4 | 4 | nothing | nothing | nothing |
| 5 | 5 | 3 | nothing | 6, 9 |
| 6 | 6 | 0, 9 | 5 | 8 |
| 7 | 3 | nothing | 1 | nothing |
| 8 | 7 | nothing | 0, 6, 9 | nothing |
| 9 | 6 | 0, 6 | 3, 5 | 8 |
A few things jump out. The 8 is the only digit that can give a match away to three different digits. The 1 and the 4 can't change shape by moving one of their own matches at all. And 0, 6 and 9 turn into each other by moving a single match, which is behind a lot of easy puzzles.
Signs work the same way. Take the upright match out of a plus and you get a minus. Put a spare match on a minus and you get a plus or an equals sign. Lay the upright match of a plus flat and the plus becomes an equals sign.
- Work out how far off the equation is.
If 5 + 7 = 5 is off by 7, you need to lose 7 on the left or gain 7 on the right. That narrows the search a lot.
- Try a change inside one digit.
Look for 0, 2, 3, 5, 6 and 9 first. They're the digits that can become another digit with a match of their own.
- Then try moving a match between two digits.
One digit gives a match away (8, 9, 6 or 7 are the usual donors) and another digit takes it (0, 1, 3, 5, 6 or 9).
- Then look at the signs.
Turning a minus into a plus needs a spare match from somewhere. Turning a plus into a minus frees one up to use on a digit.
- Last, swap the signs around.
Moving one match from the equals sign to the minus swaps them. It looks like cheating, but it's a legal move and some of the hard ones need it.
Easy puzzles
All the numbers have one digit, and most answers change only one digit.
E1
Answer to E1
5 + 1 = 6. Take the top match from the 7 and put it on the lower left side of the second 5. The 7 becomes a 1 and the second 5 becomes a 6.
E2
Answer to E2
9 − 7 = 2. Move the lower left match of the 6 to its upper right side, and the 6 becomes a 9.
E3
Answer to E3
0 + 9 = 9. Take the lower left match from the 8 and put it on the upper left side of the 3. The 8 becomes a 9 and the 3 becomes a 9.
E4
Answer to E4
2 − 2 = 0. Move the middle match of the 9 to its lower left side, and the 9 becomes a 0.
E5
Answer to E5
9 − 0 = 9. Take the lower left match from the 8 and put it on the upper left side of the 3. The 8 becomes a 9 and the 3 becomes a 9.
E6
Answer to E6
9 − 4 = 5. Move the lower left match of the 0 to the middle, and the 0 becomes a 9.
E7
Answer to E7
1 + 5 = 6. Take the lower left match from the 6 and put it on the lower left side of the 5. The 6 becomes a 5 and the 5 becomes a 6.
E8
Answer to E8
3 + 0 = 3. Move the middle match of the 9 to its lower left side, and the 9 becomes a 0.
E9
Answer to E9
5 + 4 = 9. Take the lower left match from the 6 and put it on the upper right side of the 5. The 6 becomes a 5 and the 5 becomes a 9.
E10
Answer to E10
4 − 4 = 0. Move the middle match of the 6 to its upper right side, and the 6 becomes a 0.
Medium puzzles
Now the match usually travels between a digit and a sign.
M1
Answer to M1
3 + 2 = 5. Take the lower left match from the 6 and put it on the minus. The 6 becomes a 5 and the minus becomes a plus.
M2
Answer to M2
8 − 7 = 1. Take one match from the plus and put it on the lower left side of the 9. The plus becomes a minus and the 9 becomes an 8.
M3
Answer to M3
2 = 8 − 6. Take one match from the equals sign and put it on the minus. The equals sign becomes a minus and the minus becomes an equals sign.
M4
Answer to M4
0 + 0 = 0. Take the middle match from the 8 and put it on the minus. The 8 becomes a 0 and the minus becomes a plus.
M5
Answer to M5
7 − 0 = 7. Take one match from the plus and put it on top of the 1. The plus becomes a minus and the 1 becomes a 7.
M6
Answer to M6
4 + 5 = 9. Take the lower left match from the 8 and put it on the minus. The 8 becomes a 9 and the minus becomes a plus.
M7
Answer to M7
8 − 2 = 6. Take one match from the plus and put it in the middle of the 0. The plus becomes a minus and the 0 becomes an 8.
M8
Answer to M8
1 + 5 = 6. Take the top match from the 7 and put it on the minus. The 7 becomes a 1 and the minus becomes a plus.
M9
Answer to M9
8 − 8 = 0. Take one match from the plus and put it on the upper right side of the 6. The plus becomes a minus and the 6 becomes an 8.
M10
Answer to M10
5 + 4 = 9. Take the lower left match from the 8 and put it on the minus. The 8 becomes a 9 and the minus becomes a plus.
Hard puzzles
Two digit numbers, and a few answers that move the equals sign itself.
H1
Answer to H1
3 + 16 = 19. Take the upper right match from the 8 and put it on the upper right side of the 5. The 8 becomes a 6 and the 5 becomes a 9.
H2
Answer to H2
10 + 19 = 29. Take the middle match from the 8 and put it on the minus. The 8 becomes a 0 and the minus becomes a plus.
H3
Answer to H3
11 − 8 = 3. Take one match from the plus and put it on the upper right side of the 6. The plus becomes a minus and the 6 becomes an 8.
H4
Answer to H4
3 = 13 − 10. Take one match from the equals sign and put it on the minus. The equals sign becomes a minus and the minus becomes an equals sign.
H5
Answer to H5
5 + 12 = 17. Move the upper right match of the 3 to its upper left side, and the 3 becomes a 5.
H6
Answer to H6
6 + 19 = 25. Take the upper right match from the 9 and put it on the upper left side of the 3. The 9 becomes a 5 and the 3 becomes a 9.
H7
Answer to H7
3 + 12 = 15. Take the upper right match from the 9 and put it on the minus. The 9 becomes a 5 and the minus becomes a plus.
H8
Answer to H8
16 − 8 = 8. Take one match from the plus and put it in the middle of the 0. The plus becomes a minus and the 0 becomes an 8.
H9
Answer to H9
2 + 13 = 15. Move the upper left match of the first 5 to its upper right side, and the 5 becomes a 3.
H10
Answer to H10
2 + 16 = 18. Take the upper right match from the 8 and put it on the lower left side of the 9. The 8 becomes a 6 and the 9 becomes an 8.
Print them
If you'd rather solve on paper, your browser's print button gives you all thirty puzzles on their own, without the answers, and the answer key below on a separate page. It also works for saving a PDF.
| Puzzle | Matches show | Answer |
|---|---|---|
| E1 | 5 + 7 = 5 | 5 + 1 = 6 |
| E2 | 6 − 7 = 2 | 9 − 7 = 2 |
| E3 | 0 + 8 = 3 | 0 + 9 = 9 |
| E4 | 2 − 2 = 9 | 2 − 2 = 0 |
| E5 | 8 − 0 = 3 | 9 − 0 = 9 |
| E6 | 0 − 4 = 5 | 9 − 4 = 5 |
| E7 | 1 + 6 = 5 | 1 + 5 = 6 |
| E8 | 3 + 9 = 3 | 3 + 0 = 3 |
| E9 | 6 + 4 = 5 | 5 + 4 = 9 |
| E10 | 4 − 4 = 6 | 4 − 4 = 0 |
| M1 | 3 − 2 = 6 | 3 + 2 = 5 |
| M2 | 9 + 7 = 1 | 8 − 7 = 1 |
| M3 | 2 − 8 = 6 | 2 = 8 − 6 |
| M4 | 0 − 8 = 0 | 0 + 0 = 0 |
| M5 | 7 + 0 = 1 | 7 − 0 = 7 |
| M6 | 4 − 5 = 8 | 4 + 5 = 9 |
| M7 | 0 + 2 = 6 | 8 − 2 = 6 |
| M8 | 7 − 5 = 6 | 1 + 5 = 6 |
| M9 | 8 + 6 = 0 | 8 − 8 = 0 |
| M10 | 5 − 4 = 8 | 5 + 4 = 9 |
| H1 | 3 + 18 = 15 | 3 + 16 = 19 |
| H2 | 18 − 19 = 29 | 10 + 19 = 29 |
| H3 | 11 + 6 = 3 | 11 − 8 = 3 |
| H4 | 3 − 13 = 10 | 3 = 13 − 10 |
| H5 | 3 + 12 = 17 | 5 + 12 = 17 |
| H6 | 6 + 13 = 29 | 6 + 19 = 25 |
| H7 | 3 − 12 = 19 | 3 + 12 = 15 |
| H8 | 16 + 0 = 8 | 16 − 8 = 8 |
| H9 | 2 + 15 = 15 | 2 + 13 = 15 |
| H10 | 2 + 18 = 19 | 2 + 16 = 18 |
Questions
Can a 1 be turned into a 7?
Yes, if the 1 stands on the right side of its space. A 7 is that 1 with a match across the top, so adding one match turns it into a 7, and taking the top match off a 7 leaves a 1.
Is it allowed to turn the equals sign into something else?
Yes, as long as the finished equation still has exactly one equals sign. Moving one match from the equals sign onto a minus swaps the two signs, and two of the puzzles here need exactly that.
What about answers like 6 + 4 ≠ 4?
Not here. A not equal sign needs a diagonal match, and the rules above don't allow diagonal matches. If you allow it, almost every puzzle gets a lazy second answer.
Why does my answer count when it isn't the one in the key?
The board checks the rules, not a stored answer. Every puzzle in this set has only one answer, but if you ever find another true equation, it still counts.
Is there an app with more of these?
Yes. My Matchstick Puzzle app for Android has 550 levels, including two match moves, add or remove puzzles and shapes, plus a daily puzzle. It follows the same rules as this page and works offline.
Can I use these in class?
Of course. Print the page and the answer key comes out on its own sheet. I only ask that you don't copy them onto another website.