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
    16 mins ago










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    15 mins ago










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    12 mins 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
    16 mins ago










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    15 mins ago










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    12 mins 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 20 mins ago









Artificial StupidityArtificial Stupidity

353110




353110








  • 2




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










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    15 mins ago










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














  • 2




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










  • $begingroup$
    @trancelocation : nice thanks!
    $endgroup$
    – Artificial Stupidity
    15 mins ago










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








2




2




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




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












$begingroup$
@trancelocation : nice thanks!
$endgroup$
– Artificial Stupidity
15 mins ago




$begingroup$
@trancelocation : nice thanks!
$endgroup$
– Artificial Stupidity
15 mins ago












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




$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
12 mins 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









$endgroup$





















    2












    $begingroup$

    Here my ones: :-)




    • $(4+4)cdotfrac{4}{4}$

    • $4cdot sqrt[4]{4cdot 4}$






    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
      6 mins 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









      $endgroup$


















        2












        $begingroup$

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



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






        share|cite|improve this answer









        $endgroup$
















          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 15 mins ago









          abc...abc...

          2,307531




          2,307531























              2












              $begingroup$

              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

              • $4cdot sqrt[4]{4cdot 4}$






              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
                6 mins ago
















              2












              $begingroup$

              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

              • $4cdot sqrt[4]{4cdot 4}$






              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
                6 mins ago














              2












              2








              2





              $begingroup$

              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

              • $4cdot sqrt[4]{4cdot 4}$






              share|cite|improve this answer









              $endgroup$



              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

              • $4cdot sqrt[4]{4cdot 4}$







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered 11 mins 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
                6 mins ago


















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
















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




              $begingroup$
              The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
              $endgroup$
              – Misha Lavrov
              6 mins 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 11 mins ago









                  Chris CulterChris Culter

                  20.3k43584




                  20.3k43584






























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