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Thread: With three 1s make 6

  1. #1
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    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
    Last edited by greg1313; Jun 1st 2019 at 09:57 AM.
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  2. #2
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    Re: With three 1s make 6

    VI
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  3. #3
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    Re: With three 1s make 6

    Quote Originally Posted by Archie View Post
    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
    Last edited by greg1313; Jun 1st 2019 at 03:39 PM.
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  4. #4
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    Re: With three 1s make 6

    What about **1 + 1 + 1 + three = 6**??
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  5. #5
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    Re: With three 1s make 6

    Quote Originally Posted by Debsta View Post
    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.
    Last edited by greg1313; Jun 2nd 2019 at 03:37 AM.
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  6. #6
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    Re: With three 1s make 6

    OK.
    Here's one: **(sqrt(1/.1 -1))!**
    Last edited by Debsta; Jun 2nd 2019 at 04:43 AM.
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  7. #7
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    Re: With three 1s make 6

    What about: **(sqrt (.1^-1 -1))! if ^ is allowed**
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  8. #8
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    Re: With three 1s make 6

    Quote Originally Posted by Debsta View Post
    OK.
    Here's one: **(sqrt(1/.1 -1))!**
    Yes on this one.
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  9. #9
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    Re: With three 1s make 6

    Quote Originally Posted by Debsta View Post
    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.
    Last edited by greg1313; Jun 2nd 2019 at 08:55 AM.
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  10. #10
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    Re: With three 1s make 6

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

    1 - .1 = .9
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  11. #11
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    Re: With three 1s make 6

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

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

    Yes! You have fulfilled the requirements of the puzzle.
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  13. #13
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    Re: With three 1s make 6

    Quote Originally Posted by Archie View Post
    VI
    For a moment I thought you were Denis McField.
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