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Math Help - Cute stuff

  1. #1
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    Cute stuff

    1^1 + 3^2 + 5^3 = 135
    1^1 + 7^2 + 5^3 = 175

    1^3 + 3^3 + 6^3 = 244
    2^3 + 4^3 + 4^3 = 136
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  2. #2
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    Nice. You should check Posamentier's Math Charmers
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  3. #3
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    Merci, WB.

    1^3 + 5^3 + 3^3 = 153

    3^3 + 7^3 + 0^3 = 370

    3^3 + 7^3 + 1^3 = 371

    4^3 + 0^3 + 7^3 = 407

    1^4 + 6^4 + 3^4 + 4^4 = 1634

    8^4 + 2^4 + 0^4 + 8^4 = 8208

    9^4 + 4^4 + 7^4 + 4^4 = 9474
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Nice!
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  5. #5
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    . . \begin{array}{ccc}<br />
4^5 + 1^5 + 5^5 + 0^5 &=& 4150 \\ \\<br />
5^5 + 4^5 + 7^5 + 4^5 + 8^5 &=& 54748 \\ \\<br />
9^5+2^5+7^5+2^5+7^5 &=& 92727 \end{array}
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  6. #6
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    . . \begin{array}{ccc}<br />
1^7 + 7^7 + 4^7 + 1^7 +7^7 + 2^7 + 5^7 \;\;=\;\; 1,\!741,\!725 \\ \\<br /> <br />
2^8 + 4^8 + 6^8 + 7^8 + 8^8 + 0^8 + 5^8 + 0^8  \;\;=\;\; 24,\!678,\!050 \\ \\<br /> <br />
4^{10}+6^{10}+7^{10}+9^{10}+3^{10}+ 0^{10} + 7^{10} + 7^{10} + 7^{10} + 4^{10}  \;\;=\;\; 4,\!679,\!307,\!774 \\ \\<br /> <br />
4! + 0! + 5! + 8! + 5! \;\;=\;\; 40,\!585 \\ \\<br /> <br />
\dfrac{3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 + 9^2}{1^2+2^2+3^2+4^2+5^2+6^2+7^2} \;\;=\;\;2 <br />
\end{array}
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  7. #7
    MHF Contributor harish21's Avatar
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    99,999,999 = \displaystyle{\left( 9 +\frac{9}{9}\right)^{9 -\frac{9}{9}} - \frac{9}{9}}
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  8. #8
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    My own, fresh off the press: 4^0 - 3^3 + 7^9 - 5^6 = 4 0 3 3 7 9 5 6
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  9. #9
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    666+6+6+6 = (6+6/6)^{(6+6+6)/6} + (6-6/6)^{(6+6+6)/6} + 6^{(6+6+6)/6}
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  10. #10
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    Quote Originally Posted by bandedkrait View Post
    666+6+6+6 = (6+6/6)^{(6+6+6)/6} + (6-6/6)^{(6+6+6)/6} + 6^{(6+6+6)/6}
    BEASTily interesting!!
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  11. #11
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    . . . \begin{array}{c}<br />
\text{Some Beastly Identities} \\ \\ \\<br />
1 + 2 + 3 + 4 + 567 + 89 \\ \\<br />
123 + 456 + 78 + 9 \\ \\<br />
9 + 87 + 6 + 543 + 21 \\ \\<br />
1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 5^3 + 4^3 + 3^3 + 2^3 + 1^3 \\ \\<br />
2^2+3^2+5^2+7^2+11^2+13^2+17^2\\<br />
^{\text{(First seven primes)}}<br />
\end{array}

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  12. #12
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    Quote Originally Posted by Wilmer View Post
    BEASTily interesting!!
    Haha . Credit goes to Prof. John Barrow. It's from his popular science book, "The Constants of Nature."
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  13. #13
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    Here's my small contribution

    16^3 + 50^3 + 33^3 = 165,033.
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  14. #14
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    10^2*2 + 10^1*5 + 10^0*4 = 254

    oh no, thats cheating isn't it.
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  15. #15
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    Quote Originally Posted by alan2 View Post
    10^2*2 + 10^1*5 + 10^0*4 = 254

    oh no, thats cheating isn't it.
    I think this is a consequence of the definition of the decimal system.
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