# With three 1s make 6

• Jun 1st 2019, 09:54 AM
greg1313
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:
http://mathhelpforum.com/math-puzzle...-make-6-a.html
• Jun 1st 2019, 11:12 AM
Archie
Re: With three 1s make 6
VI
• Jun 1st 2019, 02:52 PM
greg1313
Re: With three 1s make 6
Quote:

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
• Jun 2nd 2019, 01:02 AM
Debsta
Re: With three 1s make 6
What about **1 + 1 + 1 + three = 6**??
• Jun 2nd 2019, 03:26 AM
greg1313
Re: With three 1s make 6
Quote:

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.
• Jun 2nd 2019, 04:40 AM
Debsta
Re: With three 1s make 6
OK.
Here's one: **(sqrt(1/.1 -1))!**
• Jun 2nd 2019, 05:06 AM
Debsta
Re: With three 1s make 6
What about: **(sqrt (.1^-1 -1))! if ^ is allowed**
• Jun 2nd 2019, 08:25 AM
greg1313
Re: With three 1s make 6
Quote:

Originally Posted by Debsta
OK.
Here's one: **(sqrt(1/.1 -1))!**

Yes on this one.
• Jun 2nd 2019, 08:32 AM
greg1313
Re: With three 1s make 6
Quote:

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.
• Jun 3rd 2019, 05:56 AM
greg1313
Re: With three 1s make 6
Here is another hint for the third (last?) solution:

1 - .1 = .9
• Jun 4th 2019, 05:02 AM
Debsta
Re: With three 1s make 6
(sqrt((1-.1)/.1))!
• Jun 4th 2019, 10:18 AM
greg1313
Re: With three 1s make 6
Quote:

Originally Posted by Debsta
(sqrt((1-.1)/.1))!

Yes! You have fulfilled the requirements of the puzzle.
• Jun 10th 2019, 07:06 PM
Monoxdifly
Re: With three 1s make 6
Quote:

Originally Posted by Archie
VI

For a moment I thought you were Denis McField.