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# How do I get the numbers one through 20 only using six '1's

The integers from 1 to 20 can be represented by using six ones and the mathematical operations such as addition subtraction multiplication and division allowing for the use of parentheses exponents and decimals. Do not forget to follow the correct order of operations. Try to represent the Integers from 1 to 20 by using six '1's in the above conditions.
Example 7 = (1+1) • (1+1+1) +1

### 2 Answers by Expert Tutors

Robert A. | Certified Teacher and Engineer - Tutoring Physics, Maths, and SciencesCertified Teacher and Engineer - Tutorin...
5.0 5.0 (114 lesson ratings) (114)
0
I am not sure if this is a math problem or just a brain-twister but ...
How about doing something like this:
3-2, 2, 3, 4, 5, ... , 5+3+2, 20-9, 20-8, ... , 20-2, 5+5++9, 20
hopefully you get the idea.
I think I can do it with no ones.

Thanks for the response. I edited the question to clarify the instructions.

Deanna L. | Electrical engineering major and music lover with MIT degreeElectrical engineering major and music l...
4.9 4.9 (129 lesson ratings) (129)
-1
1: 1/1+1-1+1-1
2: 1+1+1-1+1-1
3: 1/1+1+1+1-1
4: 1+1+1/1+1/1
5: 1+1+1+1+1/1
6: 1+1+1+1+1+1
7:  (1+1+1)*(1+1)+1
8:  (1+1+1+1)*(1+1)
9:  (1+1+1)*(1+1+1)
10: (1+1+1)^(1+1)+1
11:  11-11+11
12: 11+1/1
13: 11+1+1
14: (1110) base (1+1/1)
15: (1111) base (1+1)
16: (1+1+1+1)^(1+1)
17: (101) base (1+1+1+1)
18: (10010) base (1/1+1/1)
19: (10011) base (1/1+1)
20: (10100) base (1/1+1/1)

You didn't say not to use zeros so I could use bases right?

That was fun..