Are there any other shorter expressions for 8 by manipulating exactly 4 4?












1












$begingroup$


The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.



enter image description here



Are there such expressions?






integer-partitions







share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    What about $(4+4)cdotfrac{4}{4}$? :-D
    $endgroup$
    – trancelocation
    1 hour ago










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    1 hour ago










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    1 hour ago
















1












$begingroup$


The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.



enter image description here



Are there such expressions?






integer-partitions







share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    What about $(4+4)cdotfrac{4}{4}$? :-D
    $endgroup$
    – trancelocation
    1 hour ago










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    1 hour ago










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    1 hour ago














1












1








1





$begingroup$


The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.



enter image description here



Are there such expressions?






integer-partitions







share|cite|improve this question









$endgroup$




The label $4times 4 -4 -4$ for 8 seems to be too long. I am looking for other shorter ones while maintaining the constraint of only using four 4.



enter image description here



Are there such expressions?






integer-partitions




integer-partitions






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 1 hour ago









Artificial StupidityArtificial Stupidity

355110




355110








  • 2




    $begingroup$
    What about $(4+4)cdotfrac{4}{4}$? :-D
    $endgroup$
    – trancelocation
    1 hour ago










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    1 hour ago










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    1 hour ago














  • 2




    $begingroup$
    What about $(4+4)cdotfrac{4}{4}$? :-D
    $endgroup$
    – trancelocation
    1 hour ago










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    1 hour ago










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    1 hour ago








2




2




$begingroup$
What about $(4+4)cdotfrac{4}{4}$? :-D
$endgroup$
– trancelocation
1 hour ago




$begingroup$
What about $(4+4)cdotfrac{4}{4}$? :-D
$endgroup$
– trancelocation
1 hour ago












$begingroup$
@trancelocation : nice thanks!
$endgroup$
– Artificial Stupidity
1 hour ago




$begingroup$
@trancelocation : nice thanks!
$endgroup$
– Artificial Stupidity
1 hour ago












$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
1 hour ago




$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
1 hour ago










3 Answers
3






active

oldest

votes


















2












$begingroup$

Here is one: $frac{4times4}4+4=8$



Here is another one: $frac{4!}{4-frac44}=8$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    I accept this answer because the second is relatively short.
    $endgroup$
    – Artificial Stupidity
    1 hour ago



















2












$begingroup$

Here my ones: :-)




  • $(4+4)timesfrac{4}{4}$

  • $4times sqrt[4]{4times 4}$






share|cite|improve this answer











$endgroup$













  • $begingroup$
    The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
    $endgroup$
    – Misha Lavrov
    1 hour ago










  • $begingroup$
    @MishaLavrov right. adjusted accordingly. :-)
    $endgroup$
    – trancelocation
    1 hour ago



















1












$begingroup$

We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.



Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.






share|cite|improve this answer









$endgroup$













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    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    2












    $begingroup$

    Here is one: $frac{4times4}4+4=8$



    Here is another one: $frac{4!}{4-frac44}=8$






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      I accept this answer because the second is relatively short.
      $endgroup$
      – Artificial Stupidity
      1 hour ago
















    2












    $begingroup$

    Here is one: $frac{4times4}4+4=8$



    Here is another one: $frac{4!}{4-frac44}=8$






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      I accept this answer because the second is relatively short.
      $endgroup$
      – Artificial Stupidity
      1 hour ago














    2












    2








    2





    $begingroup$

    Here is one: $frac{4times4}4+4=8$



    Here is another one: $frac{4!}{4-frac44}=8$






    share|cite|improve this answer









    $endgroup$



    Here is one: $frac{4times4}4+4=8$



    Here is another one: $frac{4!}{4-frac44}=8$







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 1 hour ago









    abc...abc...

    2,337532




    2,337532












    • $begingroup$
      I accept this answer because the second is relatively short.
      $endgroup$
      – Artificial Stupidity
      1 hour ago


















    • $begingroup$
      I accept this answer because the second is relatively short.
      $endgroup$
      – Artificial Stupidity
      1 hour ago
















    $begingroup$
    I accept this answer because the second is relatively short.
    $endgroup$
    – Artificial Stupidity
    1 hour ago




    $begingroup$
    I accept this answer because the second is relatively short.
    $endgroup$
    – Artificial Stupidity
    1 hour ago











    2












    $begingroup$

    Here my ones: :-)




    • $(4+4)timesfrac{4}{4}$

    • $4times sqrt[4]{4times 4}$






    share|cite|improve this answer











    $endgroup$













    • $begingroup$
      The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
      $endgroup$
      – Misha Lavrov
      1 hour ago










    • $begingroup$
      @MishaLavrov right. adjusted accordingly. :-)
      $endgroup$
      – trancelocation
      1 hour ago
















    2












    $begingroup$

    Here my ones: :-)




    • $(4+4)timesfrac{4}{4}$

    • $4times sqrt[4]{4times 4}$






    share|cite|improve this answer











    $endgroup$













    • $begingroup$
      The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
      $endgroup$
      – Misha Lavrov
      1 hour ago










    • $begingroup$
      @MishaLavrov right. adjusted accordingly. :-)
      $endgroup$
      – trancelocation
      1 hour ago














    2












    2








    2





    $begingroup$

    Here my ones: :-)




    • $(4+4)timesfrac{4}{4}$

    • $4times sqrt[4]{4times 4}$






    share|cite|improve this answer











    $endgroup$



    Here my ones: :-)




    • $(4+4)timesfrac{4}{4}$

    • $4times sqrt[4]{4times 4}$







    share|cite|improve this answer














    share|cite|improve this answer



    share|cite|improve this answer








    edited 1 hour ago

























    answered 1 hour ago









    trancelocationtrancelocation

    10.5k1722




    10.5k1722












    • $begingroup$
      The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
      $endgroup$
      – Misha Lavrov
      1 hour ago










    • $begingroup$
      @MishaLavrov right. adjusted accordingly. :-)
      $endgroup$
      – trancelocation
      1 hour ago


















    • $begingroup$
      The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
      $endgroup$
      – Misha Lavrov
      1 hour ago










    • $begingroup$
      @MishaLavrov right. adjusted accordingly. :-)
      $endgroup$
      – trancelocation
      1 hour ago
















    $begingroup$
    The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
    $endgroup$
    – Misha Lavrov
    1 hour ago




    $begingroup$
    The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
    $endgroup$
    – Misha Lavrov
    1 hour ago












    $begingroup$
    @MishaLavrov right. adjusted accordingly. :-)
    $endgroup$
    – trancelocation
    1 hour ago




    $begingroup$
    @MishaLavrov right. adjusted accordingly. :-)
    $endgroup$
    – trancelocation
    1 hour ago











    1












    $begingroup$

    We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.



    Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.



      Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.



        Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.






        share|cite|improve this answer









        $endgroup$



        We have $8=4+4^{4/4}$, which plays nicely with your existing $4=4+4^{4-4}$.



        Edit: Or $8=4+log_4 4^4=log_4 4^{4+4}$, if you want to bring in a new ingredient.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 1 hour ago









        Chris CulterChris Culter

        20.4k43584




        20.4k43584






























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