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Math Help - Four 4's: Urgent help needed

  1. #1
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    Question Four 4's: Urgent help needed

    Hey all,

    I could really use some help with this one:

    Using four 4's and any combination of math operations, represent as many of the whole numbers 1-100 as you can.

    I found operations that result in: 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 16, 20, 24, 36, 60, 64, 65, 68, and 72.

    I am having a tough time finding the others from 1 through 100. Any help will be greatly appreciated.

    Thanks,
    cheyanne
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  2. #2
    Super Member wingless's Avatar
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    \frac {4^4}{4+4} = 32
    4*4 + \frac {4}{4} = 17
    4*4 - \frac {4}{4} = 15
    4*(4+4) - 4 = 28
    4 + 4 - \frac {4}{4} = 7
    4! + 4 + 4 - 4 = 28
    4! + 4 + \frac {4}{4} = 29
    4! + 4 - \frac {4}{4} = 27
    {{4+4} \choose {4}} + 4 = 74
    {{4+4} \choose {4}} - 4 = 66
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  3. #3
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    Hello, cheyanne!

    Using four 4's and any combination of math operations,
    represent as many of the whole numbers 1-100 as you can.
    This is a classic (very old) problem . . .


    Here are some tricks you may wish to explore . . .

    . . \frac{4}{.4} \:=\:10

    . . \frac{4!}{.4} \:=\:60



    One of the hardest is: . \frac{4!+ 4.4}{.4} \;=\;71


    One of my students came up with: . \frac{\left(\dfrac{4}{.4}\right)!}{(4+4)!} \;=\;90

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  4. #4
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    Quote Originally Posted by cheyanne View Post
    Hey all,

    I could really use some help with this one:

    Using four 4's and any combination of math operations, represent as many of the whole numbers 1-100 as you can.

    I found operations that result in: 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 16, 20, 24, 36, 60, 64, 65, 68, and 72.
    Hello,

    here are some of the missing numbers:

    14=\left(\sqrt{4}+\sqrt{4}\right)^{\sqrt{4}}-\sqrt{4}

    18= 4 \cdot 4 + \frac4{\sqrt{4}}

    19 = 4! - 4 - \frac44

    21 = 4! - 4 + \frac44

    23 = 4! - \frac{\sqrt{4} + \sqrt{4}}{4}

    25 = \left(4 + \frac44 \right)^{\sqrt{4}}
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  5. #5
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    Hello, everyone!


    Did you know there is an Ultimate Solution to the "Four four's"?

    Check this out . . .


    n \;=\;-\log_{\left(\frac{4}{\sqrt{4}}\right)} \left[\log_4\left(\sqrt{\sqrt{\sqrt{\cdots\sqrt{4}}}}\ri  ght)\right]
    . . . . . . . . . . . . . . . .
    n radicals

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