# Can you solve the following equation by moving exactly 3 matchsticks? [closed]

If yes, how? (every line is a matchstick)

+---------        |       |        |                 +---------+
|                 |       |        |                 |         |
|                 |       |        |   -----------   |         |
+--------+   -----+-----  +--------+                 +---------+
|        |                |   -----------   |         |
|        |                |                 |         |
---------+        |                |                 +---------+
Rules:

• There is space beyond the edges, they don't wrap.
• Although this isn't tagged , out-of-the-box thoughts are welcome as well.
• I really want many answers, really. It's not a problem here, Emrakul. Jul 14, 2016 at 9:37
• If you're looking for many answers, that suggests that the question really is too broad.
– user20
Jul 14, 2016 at 14:49
• @Emrakul I.e. many out-of-the-box thoughts. Also, it's not a usual Q&A site here, so I thought of letting people answer their own way. Jul 14, 2016 at 15:10
• Questions still need to have a sufficiently limited range of answers to be a good fit for Puzzling. Incorrect guesses are fine - it's when a large number of answers fit the question that it becomes a problem.
– user20
Jul 14, 2016 at 15:38
• @Emrakul Move 3 matches, that's all. No 2 matches, no 4 matches! 3, and only 3! Jul 14, 2016 at 16:00

15 - 7 = 8
Where the 7 is the sort where the top-left vertical is present.
Move the two vertical matches of the + to make a 1 to the left of the 5. And move the 4's one horizontal upwards to make the 7's top horizontal. So I move 3 matches.

Visualization:
. +--------- A | | +---------+
. | A | | | |
. | A | | ----------- | |
. +--------+ -----+----- +CCCCCCCC+ +---------+
. | B | ----------- | |
. | B | | |
. ---------+ B | +---------+

Becomes:
. A +--------- +CCCCCCCC+ +---------+
. A | | | | |
. A | | | ----------- | |
. + +--------+ ----------- | + +---------+
. B | | ----------- | |
. B | | | |
. B ---------+ | +---------+

• Re-accepted, I now realized this is the first correct one. Jul 13, 2016 at 20:31
• This answer is not correct. 7 does not wrap around like that on a digital screen. Jul 13, 2016 at 20:43
• @TheGreatDuck It's not a seven-segment display default 7, but the puzzle did not ask for the numbers to follow the seven-segment display default numbers. Jul 13, 2016 at 20:46
• @TheGreatDuck: I've seen 7s displayed like that on 7-segment displays before.
– Deusovi
Jul 13, 2016 at 20:48
• I edited the answer to add visualization, but in the review section for the edit, the "rendered output" looks like the ASCII art doesn't line up, however looking at my edit here, it does line up perfectly. Jul 13, 2016 at 20:49

Here's how I would do it:

5 + 0 = 5. Take two sticks from the 8, give them to the 4, and move one of the 4's sticks to turn it into a 0.

• This answer seems more correct than the other. Jul 13, 2016 at 20:41
• This answer doesn't rely on ambiguity or niche facts like a nonstandard 7SD. Much better, should be accepted.
– Nij
Jul 13, 2016 at 22:38
• It might seem to be an obvious answer, and we must not forget "Simple is better than complex..." :) Jul 15, 2016 at 13:57

I can do it in one.

$5 + 4 \equiv 9$

Edit: Because there appears to be a discussion going on in the comments of this answer, I have moved my comment up here:

If you want me to move three sticks, then pick up any two matchsticks and swap them.

• Brilliant! +1 good job Jul 13, 2016 at 20:43
• This question asks for the case iff 3 matchsticks are moved. This does not answer the question. Jul 13, 2016 at 22:45
• If you nudge the two sticks that form the = up a little, and add the third one below them, you have moved three. Jul 14, 2016 at 5:15
• @PeregrineRook Nope, LaTeX is not your advisor here. The equal sign can be nudged, if there is no reason specified in the answer. Jul 14, 2016 at 9:39
• If you want me to move three sticks, then pick up any two matchsticks and swap them. Jul 14, 2016 at 13:54

Here's my solution:

Turn 5 + 4 = 8 into 9 - 9 = 0, by moving two matchsticks from the plus sign and one from the number eight.

Visualization:
. +--------- A | | +---------+
. | A | | | |
. | A | | ----------- | |
. +--------+ -----+----- +--------+ +CCCCCCCCC+
. | B | ----------- | |
. | B | | |
. ---------+ B | +---------+

Becomes:
. +--------+ +BBBBBBBB+ +---------+
. | A | | | |
. | A | | ----------- | |
. +--------+ ----------- +--------+ + +
. | | ----------- | |
. | | | |
. ---------+ CCCCCCCCC+ +---------+

Here's a solution by moving two matchsticks. (By the way, after having come up with this solution I realized that the puzzle asks for the movement of exactly three matchsticks rather than two, so I'll keep thinking.)

Change 5 + 4 = 8 to 5 + 4 > 8
You do this by changing the angle of the two matchsticks making up the = sign so that they make a > sign.

• The three are not that simple :) Jul 13, 2016 at 20:15
• Besides, since the question title says "Can you solve the following equation ...", an answer that is not an equation might be seen as being out of bounds. Jul 14, 2016 at 5:19
• Well, either way, you can see my actual (legal) answer above this one (or below if this had gotten voted higher over time). I just thought this was a cool solution despite not following the instructions, so I won't delete it. And as I said in the text above, originally I had thought the question only asked for the movement of two matchsticks, not three. I only realized it required three once I had finished writing this solution up. Edit: Forgot to @ you, oh well. @PeregrineRook Jul 14, 2016 at 6:27
• @SpiritFryer Just a reminder on @ mentions: The last commenter and the author will be notified, if you don't supply any @. If you supply an @, the author and previous commenters having the same first 3 characters as in the @ will be notified (not necessarily the last commenter) (@abcd will notify abcd and abce and abc, if they were previous commenters). You can also sometimes notify only the author with this notation. Jul 14, 2016 at 18:04

I can do it in 4.

Move the top left of the 4, to bottom left of 5, making a 6. Move the horizontal bar of the 4 up, making a 7. Move the two left verticals of the 8 to the left, Making it 13.

• Nice one, but you need to do it in 3 movements, not 2. Jul 13, 2016 at 20:26
• Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out. Jul 14, 2016 at 0:13
• @WernerCD Are you trying to learn some kind of Old English here??? Anyways, I think some people will have trouble understanding your comment (You mustn't count 4 or 2, you must count 3. Five is right out.) Jul 14, 2016 at 18:08
• youtube.com/watch?v=xOrgLj9lOwk Skip ahead to 48 seconds Jul 14, 2016 at 18:32

15 - 9 = 6

From

. +--------- | | | +---------+
. | 1 | | | |
. | | | | ----------- | 3
. +--------+ -----+----- +--------+ +---------+
. | | | ----------- | |
. | 2 | | |
. ---------+ | | +---------+

becomes

. + +--------- +---3----+ +---------+
. 1 | | | |
. | | | | ----------- |
. + +--------+ -----+----- +--------+ +---------+
. | | | ----------- | |
. 2 | | | |
. + ---------+ | +---------+

This is actually quite simple:

9 - 3 = 6 Vertical match from + sign goes to 5 to create 9. Left vertical match from 4 is placed horizontally on top to make it more like 3. Top right vertical match from 8 is placed on the bottom of ex-4 to make it a 3.

• The plus sign is 4 matches, not 2. Jul 13, 2016 at 20:40
• If someone downvoted that, I would like to know why. Jul 13, 2016 at 20:40
• @ChrisCudmore Hmm. I could see the reasoning behind that, though, in my opinion, in the original post it looks more like 3, not 4. Jul 13, 2016 at 20:42
• I originally thought the plus sign was made with 2 matches instead of 4 as well. Jul 13, 2016 at 20:57
+------         |         ------+             +-------+
|               |               |    ------   |       |
+-----+    -----+-----    ------+    ------   +-------+
|     |         |               |                     |
+-----+         |         ------+                     |

+---------                +--------+                 +---------+
|                                  |                           |
|                                  |   -----------             |
+--------+   -----+-----  +--------+                 +---------+
|        |                         |   -----------             |
|        |                         |                           |
+--------+                ---------+                 +---------+

Change 5 to 0 by removing the middle horizontal match down vertically and removing the 4's horizontal match to add it to right bottom side it to close it to 0.
Move the right vertical match of 4 to leave it as 1. add it to = in a crossed pattern.
$$0+1 \not=8$$

• Sorry I don't know how to format it to hide the text. Jul 13, 2016 at 23:43
• I added them for you, but you'll need to accept the edit. You do it by adding a >! at the start of each line that you want to be hidden. Jul 14, 2016 at 6:34