# Make 37+32=55 correct by moving one match

Move $1$ match and make this correct.

• You can't break the match.
• You can't make an inequality sign, just change numbers and/or operators.
• Are there any restrictions on what kind of answers are acceptable? I was about to make the same suggestion as El-Guest, but he got there first. Commented Aug 17, 2018 at 17:53
• my sister said //dont break the match, dont make inequality sign, just change numbers or operator// Commented Aug 17, 2018 at 18:07
• Maybe greater than sign. Although this is probably cheating too. Commented Aug 17, 2018 at 18:15
• @underds Would you mind providing a source for this problem, since it is not your own? Commented Aug 17, 2018 at 18:15
• Is there actually a known (and valid) solution? Commented Aug 18, 2018 at 23:14

Super easy:

37 - 32 = 5 | 5

Where:

the | is bitwise OR operator

By:

moving the vertical match from the plus sign to the middle of the 55

• I have a feeling this is technically the correct answer per the move one match stick requirement. Commented Aug 18, 2018 at 2:52
• Which is, of course, the best kind of correct. Commented Aug 18, 2018 at 4:28
• I know you mean 37 - 32 = (5 | 5), but I cannot help seeing it as (37 - 32 = 5) | 5, but maybe because that is because I am used to a programming language with a particular convention for operator precedence. I like the interpretation that 5 | 5 means 5 divides 5 (evenly), better. Commented Aug 18, 2018 at 10:52
• @Jeppe, which language? In C, | has higher precedence than =. Commented Aug 18, 2018 at 21:57
• @Jeppe I get that; however the symbol actually used is =, so it looks perfectly natural from another fellow programmer :) Commented Aug 18, 2018 at 22:15

A little of a stretch but

$87 - 32 = 55$

by

moving the upright + matchstick to the left of the 3 in 37

• Pun not intended, but great anyway Commented Aug 17, 2018 at 18:26
• Stretch, as in stretching the matchstick? (+1 from me) Edit: but you got the upvote because of the sweet pun! Commented Aug 17, 2018 at 18:26
• You must hold the match closer to your face to see it span the whole number. Commented Aug 17, 2018 at 22:12
• @tyobrien : indeed, the question doesn't specify you can only move it in two dimensions!
– vsz
Commented Aug 20, 2018 at 6:14
• The funkily-drawn number solution is not unique. Remove the bottom match from the last 5, resulting in a funky 9. Use this match to change the first 5 into a 6, resulting in 37+32=69. Commented Aug 21, 2018 at 13:01

Technically, you could change this to

$37 - 32 \neq 55$

by

moving the cross stick in the plus sign to go diagonally across the equals sign.

• Well if that were true you could also rot13(zbir bar sebz gur rdhnyf fvta gheavat svsgl svir vagb avargl svir; guvf jbhyq or gehr fvapr rkcerffvbaf ner arvgure gehr abe snyfr)! Commented Aug 17, 2018 at 18:06
• That sounds like another variation of the CheaterPants-You-Can't-Do-That solution, I like it! Commented Aug 17, 2018 at 18:09
• It looks even better if you rot13(zbir gur yrsg fgvpx va gur bqq-ybbxvat frira gb sbez gur vardhnyvgl fvta.)
– HKOB
Commented Aug 18, 2018 at 10:06
• That way you could solve any match puzzle involving numbers. Commented Aug 18, 2018 at 15:47
• That's what I thought. Commented Aug 19, 2018 at 10:52

Just to prove that this is impossible (without some creativity), I wrote a python script to solve these:

subs = {'1':[],'2':[],'3':[],'4':[],'5':[],'6':['5'],'7':['1'],'8':['6','9','0'],'9':['3','5'],'0':[],'+':['-'],'-':[],'=':['-']}

noop = {'1':[],'2':['3'],'3':['2','5'],'4':[],'5':['3'],'6':['9','0'],'7':[],'8':[],'9':['6','0'],'0':['9','6'],'+':['='],'-':[],'=':['+']}

ts = list("37+32=55")
alt_strings = []

for i, c in enumerate(ts):
for new_char in noop[c]:
alt_strings.append(ts[:i]+[new_char]+ts[i+1:])

for sub_c in subs[c]:
for i2, c2 in enumerate(ts):
s = [x for x in ts]
s[i] = sub_c
alt_strings.append(s)

alt_strings = [''.join(x) for x in alt_strings]
print alt_strings

for alt_string in alt_strings:
split_strings = alt_string.split('=')
if len(split_strings) != 2:
continue

left = eval(split_strings[0])
right = eval(split_strings[1])
if left == right:
print alt_string


The possible combinations I got were:

['27+32=55', '57+32=55', '91+32=55', '31+92=55', '31+32=65', '31+32=95', '31+32=56', '31+32=59', '37=32=55', '97-32=55', '37-92=55', '37-32=65', '37-32=95', '37-32=56', '37-32=59', '37+22=55', '37+52=55', '37+33=55', '37+32+55', '97+32-55', '37+92-55', '37+32-65', '37+32-95', '37+32-56', '37+32-59', '37+32=35', '37+32=53']


And there were no matches (hehe).

• As with the above (Bennett's comment)...+1 for the excellent pun (and the cool programming solution too, I guess Commented Aug 17, 2018 at 20:39
• @tyobrien how would you make the first number a 67? Commented Aug 17, 2018 at 22:24
• Noop 3 can also turn into a 9, btw, if you don't have a segment on the bottom Commented Aug 18, 2018 at 0:27
• and 7 into 4. and how does 7->1 (I can see 11)?
– JMP
Commented Aug 18, 2018 at 4:06
• You can also remove the left vertical match from 7 to keep it as 7. Commented Aug 18, 2018 at 9:28

37+32>55

There you go,

just change the equals sign to a more than sign!

-edit

You take the

vertical match from the plus sign

and

use it to burn the first five in 55

to make

37 - 32 = 5

If only the first 5 would be a 6. That would help a lot. Please ask your sister for the solution and double check if it's actually possible. Because I have a hunch that this puzzle is impossible.

• You need to move two matches to accomplish this; otherwise you end up with an implied greater than or equal sign which is also not true. Commented Aug 17, 2018 at 18:30
• Greater than OR equal to, is true too.
– Alto
Commented Aug 17, 2018 at 18:36
• Sorry about that, was a typo and it got cut-off. It is also true, but is not the full sign. Commented Aug 17, 2018 at 18:41
• I figure you haven't read all the comments, but I've mentioned both of these in comments above. Great minds think alike I guess. Commented Aug 17, 2018 at 18:59
• I like your second solution. It's not the inequality cheat, and you do move one match only, haha. +1 for that. Commented Aug 18, 2018 at 9:23

I saw this in "hot network questions" and tried to solve it on paper before I clicked to avoid getting spoiled. So I scribbled down the equation. When I couldn't find a way to solve it, I finally opened the question and saw, that my 7 had one less matchstick (the very left one). So I wondered about the display of numbers we don't get to see. Would a 9 without an underscore be legal for example? It clearly would be a distinct nine, wheter the bottom stick is there or not. You wouldn't return your 80's alarm clock because of such a nine, anyway.

Along this line of thinking I came up with this solution:

37 + 32 = 69 by taking the bottom matchstick from the second five to make the first five a six. Granted, the resulting nine is somewhat weird, but you clearly would not assume another number instead of it. Maybe for arguments sake just now, but not if some hot girl wrote the nines of her phone number in that way. That would probably just be a-okay for you. So just give me the correct flag now. Thanks.

• To further my point, here is a list of fonts in which the nines have no "back". This is from dafont.com and I just clicked through the scifi-section. imgur.com/a/8OuHuIB Occasionally (e.g. in font fabricate) you might mistake the five for a nine, but there is no way to confuse a nine with something else. As you can clearIy see: I really want this. Commented Aug 18, 2018 at 4:56
• I get the feeling that this is most likely the correct solution, especially after reading the thread on twitter (see comments under OP's post). Since it's a Korean riddle I wouldn't put it past them to use numbers that look slightly differently.
– Alex
Commented Aug 22, 2018 at 7:21

Ok here is one I don't think has appeared yet:

$37-32=1^5 5$

Explanation:

Take the vertical stick in the $+$ turning it into a $-$ and put left-below the first $5$ to get $_15\,5$. Interpret this as $1^55=5$.

• This is my new favourite for applying more than simple arithmetic. Commented Aug 21, 2018 at 15:37

Outside the box solution!

Remove the match on the + to make it a -, then eat it. Then crop the picture so that it cuts out the last 5. 37 - 32 = 5, only one match (and the frame of the picture) has moved.

• Great solution, although ...you eat matches? Commented Aug 17, 2018 at 18:23
• I tell other people to eat matches. I find it improves my quality of life substantially. Commented Aug 17, 2018 at 18:24
• Or even better rot13(yvtug gur zngpu naq ohea gur bgure 5) Commented Aug 17, 2018 at 18:30
• @BennettBernardoni out of all the answers we've put forward, this one in the comments might be my favourite so far Commented Aug 17, 2018 at 18:32
• Btw: rot13(Vs lbh vagraq gb pebc gur cvpgher naljnl lbh zvtug nf jryy zbir gur zngpu vagb gur ynfg svir vafgrnq bs rngvat vg, perngvat n fvk.)
– Alex
Commented Aug 21, 2018 at 12:10

Take a match from the equal sign and put it anywhere else where it creates a number. For example: 37 + 92 - 55. It's neither true nor false and it's left to the reader to calculate!

• In fact, as the resulting expression is non-0 , many programming languages would say it is indeed true. Commented Aug 20, 2018 at 12:29

The extra match on the 7 seems suspicious, so I assume the solution is:

Removing the extra match from 7, breaking it in half and making it 69 in the other end:

Even better:

If you can split the match vertically :)

• From the comments: no splitting of the match! Commented Aug 22, 2018 at 12:06

17 + 3e = 55

Of course, it makes a weird looking one...

_  _      _  _      _  _
|| | _|_ _||_| -- |_ |_
_|  |  |  _||_  --  _| _|

• Make sure to hide your answer in spoiler quotes >!, but $(+1)$ anyway :) Commented Aug 19, 2018 at 13:36
• I tried to hide it, but no amount of >! and <pre><code> tags would allow the code block to remain lined up in the spoiler quote. Is there a good way of doing that?
– BM-
Commented Aug 20, 2018 at 1:40
• There you go @BM-: note the \s which stop italicisation. Commented Aug 20, 2018 at 22:15
• Of course! Thank you, I hadn't though of that.
– BM-
Commented Aug 20, 2018 at 23:11

My contribution to the answer pile:

Take the upper left match on the 7 so that it's still a 7. Put the match on top of the equals sign, so that it and the upper part of the equals sign form an angle. Like this:

The result looks a bit sloppy, but it can be read as

$37+32 \geq 55$

The inequality is technically correct, which is the best kind of correct.

• *Technically*, the equation is not technically correct, it is the (rot13) *vardhnyvgl* which is correct. Commented Aug 20, 2018 at 22:19
• @boboquack Thanks for pointing that out, I edited my answer Commented Aug 20, 2018 at 23:50

You can either interpret that as a zero or a five that's been slashed out.

My answer, similar to @alto's, is a little bit more elegant.

Take the leftmost downstroke from the 7 and place it at an angle above and and touching the top bar of the = sign to form 'a greater-than-or-equal' (or less-than-or-equal") sign.

BTW, this brute force & ignorance approach (in Python 3.x.) shows that it is not possible without modifying the + or = chararacter:

'''  Dictionary of all possible "matchstick' substitutions.  Note that
some "matchstick" characters can be transformed into variants of
themselves by adding or removing one stroke/matchstick, e.g. 7 (by removal of
leftmost downstroke); 6 and 9 (by adding a horizontal top/bottom stroke).

SubstitutionList = {
'+':['+','-'',='], '-':['+','-'',='],     '=':['+','-'',='],
'1':['1'],         '2':['2','3','6'],     '3':['2','3',5','9'],
'4':['4','9'],     '5':['3','5','6','9'], '6':['6','9','0'],
'7':['4','7','9'], '8':['8'],             '9':['9','6','0'],
'0':['0','9','6'],
'''
''' Only these values are needed (after allowing for character variations) '''

SubstitutionList = { '2':['2','3','6'],     '3':['2','3','5','9'],
'5':['3','5','6','9'], '7':['4','7','9'],
'+':['+','-','='],     '-':['+','-','='],
'=':['+','-','='] }

TestEquation = '37+32=55'
PossibleSolutions = []   # None yet

''' For clarity the code that extracts values from "TestEquation" has been omitted  '''

for I in SubstitutionList.get( '3' )  :
for J in SubstitutionList.get( '7' ) :
for K in SubstitutionList.get( "+" ) :
for L in SubstitutionList.get( "3" ) :
for M in SubstitutionList.get( "2" ) :
for N in SubstitutionList.get( "=" ) :
for O in SubstitutionList.get( "5" ) :
for P in SubstitutionList.get( "5" ) :
Equation = I+J+K+L+M+N+O+P    # concatinate the letters into a string
FirstNumber  = int( Equation[   : 2 ] )
SecondNumber = int( Equation[ 3 : 5 ] )
ThirdNumber  = int( Equation[ 6 :   ] )
if ( (Equation[2] == '=' ) and (Equation[5] == '+' ) ) :
if ( FirstNumber  == (SecondNumber + ThirdNumber) ) :
PossibleSolutions += [ Equation ]
elif ( (Equation[2] == '=' ) and (Equation[5] == '-' ) ) :
if ( FirstNumber  == (SecondNumber - ThirdNumber)  ) :
PossibleSolutions += [ Equation ]
elif ( (Equation[2] == '+' ) and (Equation[5] == '=' ) ) :
if ( (FirstNumber + SecondNumber) == ThirdNumber  ) :
PossibleSolutions += [ Equation ]
elif ( (Equation[2] == '-' ) and (Equation[5] == '=' ) ) :
if ( (FirstNumber - SecondNumber) == ThirdNumber ) :
PossibleSolutions += [ Equation ]

OneCharacterMoves = []   # match changed position inside one character, e.g. change "3' to '2', "6" to "9" etc.
TwoCharacterMoves = []   # match moved from one character to another
for ValidEquation in PossibleSolutions :   # valid solutions change one or two characters
DifferenceCount = 0
for i, _ in enumerate( ValidEquation ) :
if ValidEquation[ i ] != TestEquation[ i ] :
DifferenceCount += 1
if ( DifferenceCount == 1 ) :
OneCharacterMoves += [ ValidEquation ]
elif ( DifferenceCount == 2 ) :
TwoCharacterMoves += [ ValidEquation ]

print( 'Original :                ', TestEquation )
print( 'Involving One Character:  ', OneCharacterMoves )
print( 'Involving Two Characters: ', TwoCharacterMoves )


The program produces :

Original :                 37+32=55
Involving One Character:   []
Involving Two Characters:  ['27+32=59', '37+22=59', '37+32=69']


Inspecting the values shows that none of them can be produced by moving one matchstick.

• It could well be argued, that the substitution-list is incomplete. Check out my answer or this font dafont.com/de/space-age.font?fpp=100&text=1234567890 and run it again to be amazed! Commented Aug 18, 2018 at 4:02
• I'm assuming we are limited to 7 segment "characters' - like the numbers on digital clocks., The code was inspired by @John Aaron. And of course I may have missed some "subtitutions" . Neat font by the way... Commented Aug 18, 2018 at 4:17
• yeah, sure. my nine would be a AFGC in that regard. en.wikipedia.org/wiki/… Wikipedia basically says "uncommon", I say "weird", but I found eight fonts that use this style of nine and in no one it could be confused with something other... I am totally going to build a picture! Commented Aug 18, 2018 at 4:25
• Changing two matches you can also get 97-32=65
– user
Commented Aug 19, 2018 at 0:05

Here's a boolean logic solution:

Take one of the $=$ matches, break it in half, and put it on the right side of the remaining = match to make a right facing arrow $\rightarrow$. Then, the LHS is $69$, interpreted as a boolean is True, and the RHS is $55$, interpreted as a boolean is True. Then, the statment True $\rightarrow$ True is True. Thus, the statement becomes True.

I think the following is technically a solution to the problem:

Make use of the fact that those are not arbitrary sticks, but matches. So, take the vertical match from the plus (making it a minus), move it quickly over the side of the match box (so it starts burning), and then move it in turn to all the matches making up the left digits (so they all catch fire and burn away, without moving). Then put that match anywhere out of the way to finish its burning without affecting the rest of the matches.

The remaining matches form the equation 7-2=5.

• Or use your idea to burn the first 5: 37 - 32 = 5. Commented Aug 21, 2018 at 5:06

Along the lines of El-Guest and Alto:

37 + 3P = 55 where P = 6.

I know that's not the answer, however; from my testing I have found that the only (to my knowledge) possible (true) combinations are:

37 + 22 = 59, 27 + 32 = 59, 57 - 22 = 35, 97 - 32 = 65, 34 + 22 = 56

But all of those require more than one match. I'll keep at it, if I solve it I'll update. All in all, I have found 210 total numeric combinations. None of which are achieved with a single move. I have written a loop in C# that goes through multiple arrays of all possible number combinations to confirm this. I may be missing something, but mathematically; this seems quite impossible, aside from the Cheater-Pants, you can't do that solutions that El-Guest and several others (including myself) have posed.

Also, not sure as to why I got a down vote as my answer evaluates true, and can be achieved with a single match:

37 + 3P = 55 evaluates true when P = 6; this breaks down to 37 + 18 = 55.

If you down vote, please explain why the down vote is justified.

• I like this answer, and thanks for the kind mention! :P (+1) from me! Commented Aug 20, 2018 at 17:04
• I liked your reference, so no problem on the mention! Your answer was the first I thought of, then several other answers that fell into the same category. I only answered because my solution had not been recommended yet, and I hadn't found any possible numeric combinations! Commented Aug 20, 2018 at 17:08

The solution appears after [re]moving a match:

37 - 32 = 5 a clue is that in second 5 match heads are aligned so that they burn each other properly until 5 is fully burnt, so perhaps we are supposed to ignite it with the match we took away.

• This is a good observation: the first 5 is drawn differently to the other numbers in that its heads are together, whereas the others are apart. Could be onto something
– Tas
Commented Aug 22, 2018 at 2:16

By moving one match to

turn the second 5 into 3 and then interpreting the suspicious "extra" match in 7 as 1

we get

317+32=53

Here is a solution exploiting that the algebraic operations are not specified in the question.

Take the vertical part of the plus sign and place it horizontally above the equality sign to obtain 37 "minus" 32 "is defined as" 55.

• That's not the symbol for "is defined as" ... ? Commented Aug 19, 2018 at 17:01
• it is used as such, see en.wikipedia.org/wiki/Triple_bar
– HRSE
Commented Aug 20, 2018 at 2:59
• Nice. The brute-force general-case approach. Commented Aug 21, 2018 at 15:39

It gives a negative value but I would like to share it anyways:

37-92 = 55

How?

Just remove the vertical match from the "+" sign and add onto 32, now it is 92.

• Where does the - in front of 55 come from?
– puck
Commented Aug 18, 2018 at 10:30
• @puck it’s not a match.. it’s negative value (-) Commented Aug 18, 2018 at 21:25
• the result is -55 not 55. To make the term match you need a minus sign in front of 55.
– puck
Commented Aug 19, 2018 at 6:52
• I like it even if it's not correct. :-)
– Alex
Commented Aug 21, 2018 at 12:16

Move the lower match of the plus and the top match moves too! Make $37\times32=1184=550\times2+84$, and the picture has been (unfairly in my opinion) cropped so that you can't see the last bit!

• Are you claiming that "0×2+84" is missing from the right part of the image? That's quite a bold claim. Commented Aug 19, 2018 at 20:24
• JonMark Perry; do you have any evidence of this? Perhaps an online sample, or the original image itself? Commented Aug 20, 2018 at 18:47
• it later struck me the cropped portion could be anything, $\times21+29$, for example, so no direct proof yet...
– JMP
Commented Aug 21, 2018 at 1:24

To combine user477343's comment with CR241's answer,

Remove the vertical match from the +, break it in half, put one half on the upper left of the first 3 to make it a 9, and the other half in front of the first 5 as a minus sign.

I know the way I constructed this pattern doesn't match the original picture, but I'm sure I nailed the right pattern.

• OP specifically says, albeit in comments "don't break the match"
– Tas
Commented Aug 22, 2018 at 2:14
• @Tas Yes, so it does. sigh Commented Aug 22, 2018 at 2:18
• Oh, kind of you to include me in your answer! $(+1)$ :P Commented Jun 24, 2019 at 10:01

The equation is actually

$$3^1 7 + 32 = 55$$

So,

$$3^1 \times 7 + 32 = 53$$ ...just turn the $55$ into a $53$ by moving one match.

Edit: Sorry, I didn't notice that Kamil posted the same answer earlier.

• Excellent - this looks to be it!
– Tom
Commented Aug 30, 2018 at 12:14
• @Tom couldn't agree more! Unfortunately, however, this is a duplicate of KamilMaciorowski's answer :\ Commented Aug 31, 2018 at 4:57
• @user477343 - good spot! Kamil posted this earlier. These solutions resolve the suspicious 1 before the 7 and give a valid equation. Nice :)
– Tom
Commented Aug 31, 2018 at 5:06

Remove the lower right matchstick to give 3 to the power of pi. Break the stick a bit and the extra matchstick on the equals to give an approximately equals symbol.

• That's two operations (removing one matchstick, breaking another), but the question requires just one. Commented Aug 19, 2018 at 17:13
• No it does not seem to mention anything about number of operations. Only one stick is bent. But then a comment says no match breaking. Commented Aug 19, 2018 at 19:31

I can only think of

$37 - 32 ≡ 55 \pmod{5}$

I have

moved the vertical bar of the $+$ sign moved to the $=$ sign to get a triple bar symbol. This turns the expression into a modular arithmetic expression.