Use four 4's to make 5 with limitations

greg1313

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May 23, 2015
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(I posted this at another site. I'm looking for any takers here. Ignore that "1." symbol below, not the instructions, though.)


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


  1. 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 (not including those for "sqrt(X)" form)

    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 [FONT=MathJax_Main-Web]√[/FONT]4 using Latex, or "sqrt(4),"
    or maybe there is the square root sign in a handy menu on this page/site.
    not sure.

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


    [FONT=MathJax_Main-Web]√[/FONT](4∗4) + 4/4 = 5

    [FONT=MathJax_Main-Web]√[/FONT]4∗[FONT=MathJax_Main-Web]√[/FONT]4 + 4/4 = 5 . . . . . . . . . which is just a variant of the one above it



    We could keep a running list of solutions.
 
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That's using 6 4's :confused:
I edited them.


And why are you using "greg1313" as name?
I'm the same person with that username that you first responded to in Math Help Forum and possibly this site.

Denis posted (with my added commentary):

Here's 7 correct ones:

sqrt(4) + sqrt(4) + 4/4 = 5 . . . . good

sqrt(4) * (sqrt(4) + 4/4 = 5 . . . . mismatched parentheses

sqrt(4*4) + 4/4 = 5 . . . . good

sqrt(4*4) + sqrt(4)/sqrt(4) = 5 . . . . good

(4*4+4) / 4 = 5 . . . . good

4/(sqrt(4)+sqrt(4)) + 4 = 5 . . . . good

(sqrt(4)+sqrt(4))/4 + 4 = 5 . . . . good
 
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\(\displaystyle \sqrt{4}\bigg( \sqrt{4} \ + \ \dfrac{ \sqrt{4}}{4}\bigg) \ = \ 5\)
 
I asked the real greg (whom I know fairly well): he never joined this site...
so I guess you're a different greg...who by luck added"1313"...
You can see next to my username that I joined here back in May 2015, but you
questioned only just recently about my username being used!? Hm.
 
4 + 4/(sqrt(4)*sqrt(4)) = 5

(sqrt(4) + 4)/sqrt(4) + sqrt(4) = 5
 
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