# find out the missing expressions [closed]

10 10 10 10 = 1
10 10 10 10 = 2
10 10 10 10 = 3
10 10 10 10 = 4
10 10 10 10 = 5
10 10 10 10 = 6
10 10 10 10 = 7
10 10 10 10 = 8
10 10 10 10 = 9
10 10 10 10 = 10

You can only add expressions, you cannot change any numbers.

## closed as too broad by Quintec, F1Krazy, athin, Rand al'Thor, GlorfindelMar 20 '18 at 15:50

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• What are the allowed mathematical operators? – Saeïdryl Mar 20 '18 at 13:53
• Hi Peggy, and welcome! When you make this kind of problems, you need to say what we can use. Is it just the symbols + - * and /, or maybe something more? (If we can use anything, then it's not a very interesting problem anymore. We already know how to solve all of those) – Bass Mar 20 '18 at 14:02
• all symbols, including brackets and roots – Peggy Mar 20 '18 at 14:38
• @Peggy Could you please give us a list of symbols? As Bass pointed, if you allow all symbols the solution is easy. – Saeïdryl Mar 20 '18 at 14:59
• I did some of them; – Peggy Mar 20 '18 at 16:28

Complete answer with "simple" operators (+, -, *, /, ⁰, ², ³, !, log):

(10 + 10) / (10 + 10) = 1
(10 / 10) + (10 / 10) = 2
(10 + 10 + 10) / 10 = 3
((10 / 10) + (10 / 10))² = 4
Another one : log(10) + log(10) + log(10) + log(10) = 4
(10 * 10) / (10 + 10) = 5
((10 + 10 + 10) / 10)! = 6 (thanks to Kepotx)
10 - 10⁰ - 10⁰ - 10⁰ = 7 (thanks to Stefano Lonati)
Another one : 10 - log(10 * 10 * 10) = 7 (thanks to Stefano Lonati)
((10 / 10) + (10 / 10))³ = 8
Another one : 10 * log(10) - log(10) - log(10) = 8 (thanks to Stefano Lonati)
((10 * 10) - 10) / 10 = 9
10 + (10 - 10) * 10 = 10

• (10 * 10) - 10 - 10 = 80, not 8 – Kepotx Mar 20 '18 at 14:10
• im not sure if we can add ^0, ^2 or ^3, isn't that adding numbers? – Kepotx Mar 20 '18 at 14:25
• @Kepotx Not really a number, it is a mathematical operator but we write it with numbers. – Saeïdryl Mar 20 '18 at 14:27
• @Kepotx Ok: 10-(log(10*10*10)) = 7 – Stefano Lonati Mar 20 '18 at 14:28
• Hi Anyone can explain the ; – Peggy Mar 20 '18 at 23:59

Thinking a little outside of the box, here's my answer:

10 + 10 + 10 + 10 != 1
10 + 10 + 10 + 10 != 2
10 + 10 + 10 + 10 != 3
10 + 10 + 10 + 10 != 4
10 + 10 + 10 + 10 != 5
10 + 10 + 10 + 10 != 6
10 + 10 + 10 + 10 != 7
10 + 10 + 10 + 10 != 8
10 + 10 + 10 + 10 != 9
10 + 10 + 10 + 10 != 10

where the operators I used were:

+ - the addition operator
! - logical NOT

This answer can be extended to any $n$ for {$n \in \mathbb N, \mathbb Z, \mathbb R, \mathbb Q\}$ with only one exception for

n = 40

• Hahahahaha, this is so clever :P – ABcDexter Mar 20 '18 at 14:05
• For anyone wondering why these types of puzzles need to be well-specified, this answer is why. – F1Krazy Mar 20 '18 at 14:09
• To be quite honest I expected this answer to be down voted, but didn't mind since it showed the OP the need to be specific – James Webster Mar 20 '18 at 14:10

Is it possible separate the number 10 in 1 and 0?

1*0+1*0+1*0+1+0 = 1
1*0+1*0+1+0+1+0 = 2
1*0+1+0+1+0+1+0 = 3
1+0+1+0+1+0+1+0 = 4
10/(1+0+1+0)+ 1*0 = 5
10/(1+0+1+0)+ 1 + 0 = 6
10-1+0-1+0-1+0 = 7
10-1+0-1+0+1*0 = 8
10-1+0+1*0+1*0 = 9
10-1*0-1*0-1*0 = 10

Or

(10 + 10) / (10 + 10) = 1
(10 / 10) + (10 / 10) = 2
(10 + 10 + 10) / 10 = 3
log(10*10) + log(10*10) = 4
(10 * 10) / (10 + 10) = 5
((10 + 10 + 10) / 10)! = 6
10 - log(10*10*10) = 7
10 * log(10) - log(10) - log(10) = 8
((10 * 10) - 10) / 10 = 9
10 + (10 - 10) * 10 = 10

• no, cant separate the all 10 numbers – Peggy Mar 20 '18 at 14:36

A simple general solution using Log, +,-,*,(),^

$$10*(10 - 10) + \log{(10^1)} = 1$$ $$10*(10 - 10) + \log{(10^2)} = 2$$ $$10*(10 - 10) + \log{(10^3)} = 3$$ $$10*(10 - 10) + \log{(10^4)} = 4$$ $$10*(10 - 10) + \log{(10^5)} = 5$$ $$10*(10 - 10) + \log{(10^6)} = 6$$ $$10*(10 - 10) + \log{(10^7)} = 7$$ $$10*(10 - 10) + \log{(10^8)} = 8$$ $$10*(10 - 10) + \log{(10^9)} = 9$$ $$10*(10 - 10) + \log{(10^{10})} = 10$$

This simple approach can generate any "n"