# Move 2 matchsticks to make the equation correct, and give 3 ways to do so

I am trying to solve the following matchsticks puzzle:

Move two matches to make the following correct: You also have to give 3 ways to do so.

Despite trying my best to solve this, I wasn't able to give 3 ways to do so. I could only think of one. Can someone please help me? Thank you.

Source: 450 multiple intelligence games that Harvard made for students puzzle book(translated, original title(in Chinese): 哈佛给学生做的450个多元智能顺练游戏)

• While I have answered this puzzle below, it would be good if you could provide the source where you found it so that the original content creator is credited. Thanks :) – Stiv Nov 16 '20 at 10:59
• @Stiv, to be honest, I really do not know who created this puzzle. I actually found it inside a Chinese puzzle book that comes from Taiwan called "450 multiple intelligence games made by Harvard for students"(the Google translation of the title). I also didn't buy it, someone gave it to me. The original title of the book(in Chinese) is "哈佛给学生做的450个多元智能顺练游戏" – Pilot Nov 16 '20 at 11:06
• Okay, maybe just mention that in the question itself following "Source:" - all non-original puzzles posted on PSE should be credited somehow, so we can avoid any messy accusations of plagiarism. I think that would probably be sufficient :) – Stiv Nov 16 '20 at 11:09

You can solve this puzzle as follows:

...producing the equations:

$$1 + 9 - 2 = 8$$
$$1 + 9 - 8 = 2$$
$$1 + 5 + 0 = 6$$

• The second solution is incredibly straightforward. – Helena Nov 17 '20 at 11:42

Three more (variations on a single theme):

Solution 1:

move the 2 vertical matches from 5 to turn 5 into a 2. and you get $$1 + 9 - 8 = 2$$

Solution 2:

remove 1 match from 9 to make it a 5 and remove the center match from 8. Add them as follows. 1 add it over the minus to make it a plus. one add it vertically to the 5 after the equal sign to make it a 6. You get $$1 + 5 + 0 = 6$$

Solution 3:

take 2 matched from the 8 transforming it to 2. Move the matches to the 5 making it an 8. You get $$1 + 9 - 2 = 8$$

Here are three more solutions different to the ones given already

Solution 1

Remove two matches like so

Then flip your screen upside down

Solution 2

Remove one match and move one match like so

Then flip your screen upside down

Solution 3

Move two matches like so

Then flip your screen upside down

All the obvious answers have been posted so here's a less orthodox one:

• This is not an equation. – Marius Nov 17 '20 at 7:21
• @Marius The puzzle says "make the equation correct". Not "make the equation a correct equation." This is correct. – Studoku Nov 17 '20 at 12:13
• exactly...and a<b is not an equation. it's an inequation. So your answer is not correct. I'm not saying the inequation is not correct...the answer is not. – Marius Nov 17 '20 at 13:35
• @Marius Where did I say a<b was an equation? – Studoku Nov 17 '20 at 13:39
• the title says "Move 2 matchsticks to make the equation correct, and give 3 ways to do so". But let's say you are right and stop this discussion, because it's not helping anyone. – Marius Nov 17 '20 at 14:17

There seems to be at least 5 different ways to make it correct. Here are the 3 ways I found:

1 + 9 - 8 = 2
1 + 8 - 6 = 3
1 + 8 - 3 = 6