# Thread: With three 1s make 6

1. ## With three 1s make 6

Use three 1s and no other digits to make an expression that equals 6.

You can use these only:

parentheses, +, -, /, *, regular factorial sign, square root symbol (or "sqrt"), decimal point (no repeating decimal use), concatenation of digits (if needed)

I am looking for at least three solutions.

This other puzzle is similar:
With three fives make 6

VI

3. ## Re: With three 1s make 6 Originally Posted by Archie VI
Yours is a solution that belongs to a different type of question that involves closer to matchsticks (maybe line segments)
for example. Mine involves digits, together with as needed operations, to form number expressions that equal 6 in base 10.

I'll offer a first solution:

Spoiler:
(1 + 1 + 1)! = 6

4. ## Re: With three 1s make 6

What about **1 + 1 + 1 + three = 6**??

5. ## Re: With three 1s make 6 Originally Posted by Debsta What about **1 + 1 + 1 + three = 6**??
The proposed solution is not allowed, in part, because that word
does not exist in the domain of the rules of the puzzle.

Here are open hints toward getting a second solution or possibly
also a third solution.

A) What is 1/.1?

B) In the first solution I revealed that 6 can be attained when
there is an expression equal to 3, likely to be inside of grouping
symbols, and then immediately followed by a factorial sign.

6. ## Re: With three 1s make 6

OK.
Here's one: **(sqrt(1/.1 -1))!**

7. ## Re: With three 1s make 6

What about: **(sqrt (.1^-1 -1))! if ^ is allowed**

8. ## Re: With three 1s make 6 Originally Posted by Debsta OK.
Here's one: **(sqrt(1/.1 -1))!**
Yes on this one.

9. ## Re: With three 1s make 6 Originally Posted by Debsta What about: **(sqrt (.1^-1 -1))! if ^ is allowed**
The operation of "^" is not allowed for my/this particular puzzle,
but I like your way of thinking.

I am looking for (at least) one more solution.

10. ## Re: With three 1s make 6

Here is another hint for the third (last?) solution:

1 - .1 = .9

11. ## Re: With three 1s make 6

(sqrt((1-.1)/.1))!

12. ## Re: With three 1s make 6 Originally Posted by Debsta (sqrt((1-.1)/.1))!

Yes! You have fulfilled the requirements of the puzzle.

13. ## Re: With three 1s make 6 Originally Posted by Archie VI
For a moment I thought you were Denis McField.