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You are given the wrong equation (made out of matchsticks) 9 + 9 = 8 and you can move at most 3 matches. Your aim is to find all possible correct equations. Selected answer will be one that discovers most correct equations first.

enter image description here

Don't forget the [lateral thinking] tag!

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    $\begingroup$ Since there's a lateral-thinking tag, would you accept answers that use matches and not pen markings? $\endgroup$ May 14, 2020 at 21:07
  • $\begingroup$ @IanMacDonald I think I would accept both! $\endgroup$
    – JKHA
    May 15, 2020 at 0:09
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    $\begingroup$ I don't think there is a correct answer to "all correct equations", as there is too many ways to interpret the question with "lateral thinking" stipulations. I also don't think it makes a particular clever puzzle, as you can just take a random match stick equation and ask people to find different solutions. $\endgroup$
    – Helena
    May 15, 2020 at 21:00
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    $\begingroup$ This is an "open-ended" puzzle in exactly the way described here; it is a game where people compete to give as many answers as possible, not a puzzle with a definitive solution. For this reason, it is off-topic for our site. $\endgroup$
    – Deusovi
    May 16, 2020 at 2:42

10 Answers 10

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$-2 + 8 = 6$ (3 moved) $3^1 + 3^1 = 6^1$ (3 moved)
$3^1 + 5^1 = 8$ (2 moved)
$8 - 8 = 0$ (2 moved)

Since it's "lateral"

Moving matches out of view, i.e. re-moving
$0 + 0 = 0$ (2 moved, 1 removed)
$0 + 9 = 9$ (1 moved, 1 removed)
$2 + 6 = 8$ (2 moved, 1 removed)
$3 + 3 = 6$ (3 removed)
$3 + 5 = 8$ (2 removed)
$3 + 6 = 9$ (1 moved, 2 removed)
$5 + 5 = 10$ (2 moved, 1 removed)
$6 + 3 = 9$ (1 moved, 2 removed)
$9 + 0 = 9$ (1 moved, 1 removed)
$9 - 0 = 9$ (1 moved, 2 removed)
$9 - 9 = 0$ (2 removed)

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  • $\begingroup$ No actually, this is part of the puzzle. You are on the way to be selected answer ;) I confounded with something else. I count 5 equations in your answer up to now ;) $\endgroup$
    – JKHA
    May 13, 2020 at 20:18
  • $\begingroup$ OK. Hidden again. $\endgroup$ May 13, 2020 at 20:21
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A 'lateral' answer:

Remove a match from the second nine and two from the eight to get 9+5=2, apparently true!

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    $\begingroup$ Haha, I didn't expect someone to catch it that fast! $\endgroup$
    – JKHA
    May 13, 2020 at 10:15
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The classical

use any match to turn the $=$ into $\neq$

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    $\begingroup$ One might argue that it is an inequality and not an equation. One might... $\endgroup$ May 13, 2020 at 18:46
  • $\begingroup$ @JoelRondeau you are right, I didn't notice that we had to produce equations $\endgroup$
    – melfnt
    May 13, 2020 at 20:26
  • $\begingroup$ I wouldn't remove the answer, though. If you do someone else will just add it and we'll go through all this over again. In fact, +1. $\endgroup$ May 13, 2020 at 20:27
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two more possibilities

-9 + 9 = 0 or +9-9=0: move middle line of 8 to form -, (move one stick from plus to form plus on the left)

9 + 6 = 15 or 6+9=15: move two sticks from 8 to form 15, move one stick from 9 to form 6

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0
3
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Another "lateral"

Rotate the equation 180 degrees. Then remove two matches from the 8, to turn it into 12.
12 = 6 + 6

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I can do it using 2 matches:

8-0=8

Solution:

Move the up-ward facing matchstick from the plus to the 9 (makes it 8) then move the middle matchstick from the second 9 to the bottom to make it a 0

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  • $\begingroup$ Correct! Can you find the other correct equations? $\endgroup$
    – JKHA
    May 13, 2020 at 10:05
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Removing 3 matches gives the following example of :

5+5=A
{ _ _ _ }
{ │_ + │_ = │_│ }
{ _│ _│ │ │ }

Moving 2 matches gives this:

9+9=18
{ _ _ _ }
{ │_│ + │_│ = │ │_│ }
{ │ │ │ │_│ }

And, combining the two methods:

9+9=12 (base 16)
{ _ _ _ }
{ │_│ + │_│ = │ _│ }
{ _│ _│ │ │_ }

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  • $\begingroup$ I'd looked for a way of moving matchsticks to get hex addition, I did not look for a way to remove matchsticks to get hex addition. $\endgroup$ May 14, 2020 at 13:55
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Another 'lateral' one:

3 + 5 == 8 (moving 2 matchsticks to turn it into a programming-style equation)

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1
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Another lateral-thinking answer:

Don't move any matches at all. $9+9=8$ is valid in $\mathbb{Z}/10\mathbb{Z}$.

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4+

Hmm...

$9+9 > 8$ (move $=$ so it is $>$)

$8 - 0=8$ (move vertical line in plus to make 9 into 8, turn 9 into 0 by moving middle line)

$9-9 ≠ 8$ (move plus sign to make not equals)

$9+9≠0$ (move 8's middle to make ≠)

You can make so many solutions just by changing the sign in the middle!*

Contributed by friends:

$-9+9=0$ (move middle of 8 to before first 9 to make -9) $5+3=8$ (remove to make 9s into 5 and 3)

*but I'm too lazy

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  • $\begingroup$ I want to put each answer on a separate line within the spoiler quote, but when I try the spoiler turns into a normal block quote. Can anyone help? $\endgroup$
    – Wezl
    May 15, 2020 at 13:12
  • $\begingroup$ Welcome to Puzzling.SE! That is a nice first answer and I helped you a little on the formatting ;) you get my upvote! $\endgroup$
    – JKHA
    May 15, 2020 at 13:13

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