# 10 + 1 − 2 = 9 X

Can you solve the puzzle in this expression?

• You must only replace the 'X' to solve this puzzle.
• You must not add, remove, rearrange or modify any of the other characters.
• 'X' represents only one single digit number.
• No maths is required.
• The solution relates to language, patterns and lateral thinking.

Hint

A puzzle that heavily depends on linguistic features; for instance it may concern foreign languages, or only work in some particular language, or be built around a peculiarity of the English language.

(The summary above was taken from the Wiki excerpt for the 'language' tag)

• Only one answer has the right number but it doesn't have the solution I'm looking for. Again the tags are particularly important, especially 'pattern', 'lateral-thinking' and 'language'. A lot of people are missing the 'pattern' part. – Ambo100 Jan 11 '18 at 18:48
• Is the answer you have in mind definitely more satisfactory than the other answers that have been given? I mean, would someone seeing your intended solution say "Ah, yes, that definitely solves it" in a way they wouldn't in response to any of the others? – Gareth McCaughan Jan 11 '18 at 20:09
• @GarethMcCaughan That is a good point and it's something I have considered. There have been some good answers so far but I have not seen one that matches all the criteria given in the question and the tags used. It is difficult to tell you for sure without giving the answer away. – Ambo100 Jan 11 '18 at 20:14
• In light of the correct answer, would the knowledge tag be appropriate? Anyone without knowledge of that particular... system... would never be able to solve this. – Lolgast Jan 12 '18 at 8:08
• As others have said, the puzzle is not an equation, nor is it a "solved equation", whatever that means. It would better asked as "find the next character in this sequence". The tags were useful however. It's a great puzzle though, just posed in a misleading manner. – gogators Jan 12 '18 at 18:15

Guess:

X = 九

because

In Chinese: 10 is 十, 1 is 一, 2 is 二, The 'equation' is translating from Arabic numbers to Chinese

• Correct! I am not sure why this answer was downvoted... – Ambo100 Jan 11 '18 at 22:24
• This has a bit of the xkcd 169 about it. I mean, the puzzle says the thing is an equation and it isn't; it includes a bunch of deliberately incorrect symbols (none of the symbols as shown in the original "equation" is correct); the final answer isn't really something anyone would write (you'd present things in a more systematic order, no?). It's clever, I guess, but I'm not left thinking "yup, that's definitely a satisfying solution". (I didn't downvote the answer; my whingeing is about the puzzle.) – Gareth McCaughan Jan 11 '18 at 22:28
• This is actually awesome haha, nice job TWhelan! My suggestion to OP (Ambo100) is that, if you want to make the question even less misleading, try to handwrite the equation on a piece of paper and pose as a picture – Alex Jan 11 '18 at 23:29
• Very clever answer... question to me seems like it could be excellent with some work. As a 25-year reader of Japanese, I don't see + - = as numerals: the font utterly differentiates them. As another reader has suggested, though, a handwritten list of 10 十 1 一 2 二 9 X would be fair enough, given that handwriting could be unclear enough to admit of either interpretation. Or, use a screenshot of a (sans serif?) font and size where using the actual characters could be taken by most viewers for mathematical signs. In other words have the right glyphs but count on them being misread. – Swiss Frank Jan 12 '18 at 7:40
• FWIW, I agree that a hand-written version of this could be much better. – Gareth McCaughan Jan 12 '18 at 12:24

I think we can use:

superscript 1

Where

$10 + 1 − 2 = 9^1 = 9$

and it is also a single digit number from Super Hint #1 (or Super 'add criteria' #1)

• If you want, here it is: ¹ – Manuel Jan 11 '18 at 18:31
• @Manuel here we go you tiny one. Thanks Manuel – Alex Jan 11 '18 at 18:32

Replace the 'X' with

1

Explanation

91 is ninety one, or nine D one, or 9d1 in dice notation, which would equal 9

• I like this because the lateral-thinking and language tags are relevant – ferret Jan 11 '18 at 18:32

Is it

2

Because

Ten plus one minus two is equal to nine too.
Or, ten plus one minus two is equal to nine, true.

• This is an interesting solution but it is not the right answer. This could be the answer to the puzzle "One plus one equals two (too)" for example or any other sum resulting in two. The exact numbers and operators used in this puzzle are very important. – Ambo100 Jan 11 '18 at 17:38

X is zero. A really small zero that is - so small it's actually a decimal point.

According to statement that is
10+1-2 = 9X
it means
10+1-2 = 9*x
now you can only replace x with 1 and answer statement is
10+1-2 = 9*1

Considering the lateral thinking tag:

X is 0

Explanation:

As we can replace X
10 + 1 − 2 = 9 X becomes 10 + 1 − 2 = 09 which is true. We replace its value and its position.

• Might run afoul of the "single-digit" rule, depending on one's interpretatin – Carl Witthoft Jan 11 '18 at 18:22
• You must not add, remove, rearrange or modify any of the existing characters, only 'X' can be replaced. – Ambo100 Jan 11 '18 at 20:36
• @Ambo100, that's not what your question states. "You must not add, remove, rearrange or modify any of the existing characters, apart from 'X'" That means you can remove, rearrange and/or modify X" – Kevin Jan 11 '18 at 20:50
• Sorry, I have clarified the question. The first point as it was before does state that the only change you can make is to replace 'X'. – Ambo100 Jan 11 '18 at 20:53
• I think re-place (in other words, "move") could be a reasonable word-play re-reading of replace. – Swiss Frank Jan 12 '18 at 7:43

X = 9?

Reasoning:

10 + 1 could be interpreted as 10 and 1 being concatenated into 101, then subtracting 2 gives you 99.

Now that math has been ruled out, maybe it's 9 because there are 9 syllables in "10 plus 1 minus 2 equals 9"?

• I like the second solution because it uses the lateral thinking and language aspect, although it is still missing a clear pattern. – Ambo100 Jan 11 '18 at 19:27

I feel like this is a super stretch but I'm going to propose it anyway.

I believe the solution for X is:

9

My thinking was:

The tags indicated language, pattern and lateral thinking. In addition, the fact that math isn't used here, I tried to not think about the numbers and symbols as math operations themselves. I decided to try and write out the line in words, seeing if I could use synonyms to try and find a pattern in the spelling that would indicate a solution.

So, I wrote:

ten (10) net (+) one (1) no (-) two (2) out (=) nine (9) ____

I noticed:

"Ten" reversed is "net". "One" reversed is close to "no". "Two" reversed is phonetically similar to "out". And, finally, "nine" reversed is close to "nine".

• A lot of the points you covered in your thinking is very good, in particular the part about not seeing the symbols as maths operators. The answer however is, as you said a stretch. – Ambo100 Jan 11 '18 at 20:27

My guess is that the answer is

1

Because

1 corresponds to a − (a horizontal line)
2 corresponds to = (two horizontal lines)
10 corresponds to + (a horizontal line and a vertical line)
9 corresponds therefore to 1 (a vertical line)

• In terms of methodology, this is the closest to the actual solution although, the 'X' is wrong. The actual solution is very much related to language, a language in particular. – Ambo100 Jan 11 '18 at 22:09

I loved this question and your tags are brilliant.

I have a very similar but different answer that you might like....

rest hidden....

So I spotted from some slight knowledge of chinnese number characters from the game Mahjong or Mah-Jong... I thought the answer could be an upside down 4 ... certainly if hand written carefully it could be done.... I like this answer as all the other numbers in the puzzle are 'arabic'

• @NL628 - too bad I didn't see this question earlier - 2 or 3 hours earlier and it would have been more relevant perhaps - still I hope this is an interesting contribution - and many thanks for the welcome – tom Jan 12 '18 at 0:44

Not quite an answer, more of a comment.

4

Where 10 is +, 1 is -, and 2 is =; Similar to TWelan's answer, which is derived from kanji, I would have assumed the kanji were just upsidedown, hence 4

• Welcome to Puzzling SE! I have noticed that you in fact, do have a different answer, so no need to say its "not quite an answer" :). This is a perfectly good answer; just a little different than the correct one. I hope you have a great time here! – NL628 Jan 11 '18 at 23:15
• Thanks! I guess I just don't like posting an answer where 99% of the effort/explanation is the same as an existing one. – Kora Jan 12 '18 at 22:10
• It's fine :))) as long as it is not an exact copy :P – NL628 Jan 13 '18 at 0:54

Note: Explanation is for the original version, but the idea does not change, just the notation. Well, taking the hints and the very specific [now deleted] comment...

I'll assume the space is significant. Thus, 9 ? is not actually a number on it's own, it's 2, similar to 9x. In other words, 9 = 9x, ergo, x = ? = 1.

• I've changed the '?' to 'X' as it was not correctly being displayed in the title, the actual symbol doesn't matter, it is simply a placeholder for the answer. – Ambo100 Jan 11 '18 at 13:24
• @Ambo100 My answer still holds in that case. Care to mention whether it is correct or not? – Lolgast Jan 11 '18 at 13:26
• Sorry, the answer is incorrect. I had checked what I had written in the body several times but it was unfortunate that when I posted the question, the space between the 9 and ? was cut out. Presumably this is some kind of automated quality filter for questions. I didn't want to have the question title and body differ as that would mislead people from the actual puzzle. – Ambo100 Jan 11 '18 at 13:29

I think the answer is 9

because

10 + 1 = 101

and

101 -2 = 99

• No maths is required to solve this puzzle. – Ambo100 Jan 11 '18 at 21:38
• This answer was already given. – gnovice Jan 11 '18 at 21:54
• @gnovice I did not see it – user Jan 11 '18 at 21:57
• Here. – gnovice Jan 11 '18 at 21:58

A two stage, very lateral solution.

10 + 1 − 2 = 9 X Can you solve the puzzle in this solved equation?

You must only replace the 'X' to solve this puzzle. You must not add, remove, rearrange or modify any of the other characters. 'X' represents only one single digit number. No maths is required. The solution relates to language, patterns and lateral thinking.

Then we replace X with:

9 (replace all instances of X)

Which leaves us with

10 + 1 − 2 = 9 9 Can you solve the puzzle in this solved equation? You must only replace the '9' to solve this puzzle. You must not add, remove, rearrange or modify any of the other characters. '9' represents only one single digit number. No maths is required. The solution relates to language, patterns and lateral thinking.

Then we simplify the left hand side and get

9 = 9 9 Can you solve the puzzle in this solved equation? You must only replace the '9' to solve this puzzle. You must not add, remove, rearrange or modify any of the other characters. '9' represents only one single digit number. No maths is required. The solution relates to language, patterns and lateral thinking.

Then we replace

9 (all instances of it) with 0 to solve this puzzle as we have 0 = 0 Can you solve the puzzle in this solved equation? You must only replace the '0' to solve this puzzle. You must not add, remove, rearrange or modify any of the other characters. '0' represents only one single digit number. No maths is required. The solution relates to language, patterns and lateral thinking.

So yes, I can solve the above equation.

This answer is technically valid, as

It invovles lateral thinking. It requires no maths (it does require arithmetic, which is very different to maths) It requires language, to know that arithmetic =/= maths

It may not be valid, if

you consider replacing 10+1-2 with 9 to be adding, removing, rearranging or modifying any of the other characters

• "arithmetic, which is very different to maths" Arithmetic is a part of mathematics. Something that requires no mathematics can't require any part of mathematics. – David Richerby Jan 12 '18 at 0:53
• @DavidRicherby there are many people who would disagree with you there. Many of these people are mathematicians. dailycaller.com/2013/06/11/… reddit.com/r/getdisciplined/comments/3oli7t/… “Arithmetic is to mathematics as spelling is to writing.” is a saying, common enough that I have no idea who to cite as the original. Go to writers.stackexchange and ask them how to spell a word, see the reception you get. – Scott Jan 12 '18 at 1:01
• Thanks but I'm a mathematician myself. The comparison with spelling is, I'm afraid, nonsense: arithmetic underpins much of mathematics in an intrinsic and unalterable way; speling iz a meer konvenshun. – David Richerby Jan 12 '18 at 1:17
• @DavidRicherby - whether it is nonsense or not is irrelevant to the question of whether my answer could have been the intended answer to the riddle. It is enough that some people claim to believe that arithmetic is not maths. Unless you can prove beyond all doubt that Ambo100 believes arithmetic to be maths, using information available at the time I posted my answer? – Scott Jan 12 '18 at 1:20
• Fine, if the question does not mean what the question says, then this could be an answer. But the usual assumption is that the question means what it says and that mistakes in the question should be corrected, not exploited. Otherwise you could just answer every question with "A mouse" and claim that the asker expressed the question "What kind of animal was Mickey?" in an incorrect way. – David Richerby Jan 12 '18 at 1:24

X = 8

because

Take the last letter of each word in "ten plus one minus two equal nine eight" and you have "nsesolet". These can can be unscrambled to spell the word noteless.

• This is not the correct answer but could you explain how the answer for X relates to the word you have? – Ambo100 Jan 11 '18 at 20:28
• Not sure how I can explain it more than I already did. – gogators Jan 11 '18 at 21:21

X = 1

because

10 + 1 - 2 = 9

same way

10 + 1 - 2 = 9 X

• ... What? How does the 1 fit in? (Note: I have myself given 1 as an answer, so I do know at least one way to fit. It's just not clear what you mean) – Lolgast Jan 12 '18 at 13:11

0

Which can be thought of as

+0 (or -0)

Giving

10 + 1 − 2 = 9 + 0 (or 9 - 0)

If you

count .0 as "representing a single-digit number" (it's a number, though usually written differently, and both as it is and in its usual form it contains just one digit)

then this yields the equation

10+1-2 = 9.0

which is true.

• Your answer uses a single-digit number which is good but there is a space between the number 9 and X so the answer would not be quite the same. Remember you cannot adjust any other part of the equation apart from replacing 'X'. – Ambo100 Jan 11 '18 at 20:10

X is

2

Making the sentence

10 + 1 − 2 = 9 2

Explanation:

The sentence is taking two series of numbers from 1 to 10: a series of even numbers (2, 4, 6, 8, 10) alternating with a series of odd numbers (1, 3, 5, 7, 9). The operator + means to raise the previous number by one step, the operator - means to lower the previous number by one step, and the operator = means to keep it the same. Since the series ends at 9 (odd) and 10 (even), 10 + and 9 + are interpreted as 2 and 1 respectively (the series starts from the beginning again). The same is true for 1 - and 2 -, which mean the next number is 9 or 10 respectively.

Therefore, when the sentence says 10 +, the next number in the even series will be 2. When it says 1 -, the next number in the odd series will be 9. When it says 2 =, the next number in the even series will stay the same. After the 9 from the odd series, the next number in the even series is 2.

• 'X' represents only one single digit number, it can not be a mathmatical symbol. – Ambo100 Jan 11 '18 at 19:23
• @Ambo100 Could you take a look at the updated answer? – b a Jan 11 '18 at 19:48
• I think I understand the explanation but this isn't the answer I'm looking for. The correct solution uses a very simple pattern. This puzzle also relates to lateral thinking and language. The tag wiki for language might give a clue. – Ambo100 Jan 11 '18 at 20:06

I would say X is

9

Because

10 + 1 is 101 - 2 is 99

It's either

3

because of

the pattern "1, 2, 3"

or

8

because of

the pattern "10, 9, 8"

.

• The first number is 10, not 1 so the pattern 1, 2, 3 would not work. This puzzle also relates to lateral thinking and language. – Ambo100 Jan 11 '18 at 19:23
• I was thinking of the consecutive 1 and 2 starting from the second number. – Micheal Johnson Jan 11 '18 at 19:58

10 + 1 − 2 = 9 X

I would say that X is 0.
10 can be written as "9 + 1" so...

9 + 1 + 1 - 2
9 + 2 - 2
9 + 0
string(9) + string(0)
90

So X is 0.

In roman numerals H has been the symbol for 200. Replace X by H and the right side will become 9H which is the hexadecimal representation for 9.

• Where did you find that H stands for roman 200? I've never heard about it, nor does a quick google show anything. In standard notation 200 is CC. – Lolgast Jan 12 '18 at 14:18
• This is apparently part of "Medieval Roman Numerals" en.wikipedia.org/wiki/… – TWhelan Jan 12 '18 at 22:56

Another possible solution that hasn't been tabled yet.

X is 9 mod 10

which makes the equation:

10 + 2 - 1 = 99 mod 10

This passes all rules, but arguably fails "No maths is required". I argue it doesn't, because

mod can be understood linguistically and in some cases interpreted with visual patterns, and one can see that by definition 9 mod 10 represents 9, and any base 10 number ZN mod 10 (N single digit) also represents N because the Z part can simply be ignored.

Replace 'X" with

$\sqrt{1}$

so it looks like this:

$10 + 1 − 2 = 9\sqrt{1}$
$9 = 9$

• X can only represent a single digit number with no other formatting, functions or operators. – Ambo100 Jan 11 '18 at 18:38

I think the answer is X = (space) So, when we replace the X with an space, it will be

# 10 + 1 − 2 = 9 X

10 + 1 − 2 = 9

• But the question says 'X' represents a single digit number. – Rand al'Thor Jan 12 '18 at 13:07
• A blank space represents 0 in some numeral systems. – TWhelan Jan 12 '18 at 15:22