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Thread: Arithmetic - - Use four 4's to make 5 with limitations

  1. #1
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    Arithmetic - - Use four 4's to make 5 with limitations

    Make an expression using exactly four 4's and no other digits.

    In order to reduce the number of solutions, I am requesting the following list of limitations.

    You can use:

    up to two addition signs

    no subtraction/negative signs

    up to one multiplication sign, "*"

    up to one division sign, "/" for a horizontal expression, or instead, use one horizontal fraction bar

    no concatenation

    up to one pair of parentheses

    no exponentiation

    up to three square root symbols

    no other roots

    no decimal points/no repeating decimals

    no factorial symbols of any type

    no other functions or characters

    - - - - - - - - - - - - - - - - - - - - - - - - - -

    For the sake of limiting solutions, these forms within a solution, or the solution itself, will be considered the same:

    A + B =
    B + A

    - - - - - - - -

    A(B + C) =
    (B + C)A =
    A(C + B) =
    (C + B)A

    - - - - - - -

    A/B + C =
    C + A/B

    - - - - - - - -

    etc.


    If you would like to write the square root of 4 in your expressions, you may want to type $ \sqrt{4}$ using Latex, or "sqrt(4),"
    or maybe there is the square root sign in a handy menu on this page/site.


    To get a couple of examples out of the way, I am starting off the list of solutions with:


    $\sqrt{4}*\sqrt{4} $ + 4/4 = 5

    $\sqrt{4*4} \ $ + 4/4 = 5 . . . . . . . . . which is just a variant of the one above it
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    Re: Arithmetic - - Use four 4's to make 5 with limitations

    Here's a gradual running list:


    $\sqrt{4}*\sqrt{4} $ + 4/4 = 5

    $\sqrt{4*4} \ $ + 4/4 = 5

    $\dfrac{4*4 \ + \ 4}{4} = 5$
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    Re: Arithmetic - - Use four 4's to make 5 with limitations

    $4+\sqrt{\dfrac{\sqrt{4\cdot 4}}{4}}$
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    Re: Arithmetic - - Use four 4's to make 5 with limitations

    Quote Originally Posted by SlipEternal View Post
    $4+\sqrt{\dfrac{\sqrt{4\cdot 4}}{4}}$
    Then there must be this simpler variant:

    $4 \ + \ \dfrac{\sqrt{4\cdot 4}}{4}$


    And, because of the three square root limit I imposed, I left myself open to this:

    $4 \ + \ \sqrt{\sqrt{\dfrac{\sqrt{4\cdot 4}}{4}}}$
    Last edited by greg1313; Jun 2nd 2018 at 10:57 AM.
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