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
    14 mins ago










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










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    10 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
    14 mins ago










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










  • $begingroup$
    Another one $4cdotsqrt[4]{4cdot 4}$.
    $endgroup$
    – trancelocation
    10 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 18 mins ago









Artificial StupidityArtificial Stupidity

353110




353110








  • 2




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










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










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














  • 2




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










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










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








2




2




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




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












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




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












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




$begingroup$
Another one $4cdotsqrt[4]{4cdot 4}$.
$endgroup$
– trancelocation
10 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









    $endgroup$













    • $begingroup$
      The first one probably looks more consistent with the others if written as $4 times frac{4+4}{4}$.
      $endgroup$
      – Misha Lavrov
      5 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









    $endgroup$













      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "69"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });














      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3089195%2fare-there-any-other-shorter-expressions-for-8-by-manipulating-exactly-4-4%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      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 13 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









              $endgroup$













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
















              2












              $begingroup$

              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

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






              share|cite









              $endgroup$













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














              2












              2








              2





              $begingroup$

              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

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






              share|cite









              $endgroup$



              Here my ones: :-)




              • $(4+4)cdotfrac{4}{4}$

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







              share|cite












              share|cite



              share|cite










              answered 9 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
                5 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
                5 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
              5 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
              5 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 10 mins ago









                  Chris CulterChris Culter

                  20.3k43584




                  20.3k43584






























                      draft saved

                      draft discarded




















































                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3089195%2fare-there-any-other-shorter-expressions-for-8-by-manipulating-exactly-4-4%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -

                      Popular posts from this blog

                      Plaza Victoria

                      Image
                      Plaza Victoria Plaza Victoria en 2017 Otros nombres Plaza de La Victoria Localización El Almendral, Valparaíso, Chile Vías adyacentes Chacabuco, Molina, Plaza Victoria y Edwards Creación 1841 Metro Bellavista Ubicación 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 Coordenadas: 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 [editar datos en Wikidata] La Plaza Victoria , también llamada Plaza de la Victoria , [ 1 ] ​ es una plaza ubicada en el sector El Almendral del plan de la ciudad de Valparaíso, Chile, de importancia patrimonial, que incluye valiosas estatuas y especies vegetales. [ 2 ] ​ La plaza se creó como tal en la primera mitad del siglo XIX, tomando previamente los nombres de Plaza Nueva y Plaza de Orrego . Si bien desde sus inicios tuvo relevancia histórica, no fue sino a partir de fines de los años 1860 cuando comenzó a cobrar mayor importancia y se convirtió en uno de los principales centros sociales de l
                      Read more

                      In PowerPoint, is there a keyboard shortcut for bulleted / numbered list?

                      Image
                      .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 2 OneNote has two useful keyboard shortcuts for bulleted and numbered lists, namely Ctrl + . and Ctrl + - . Is there something similar for PowerPoint where the work with lists is also very common? Haven't found anything here: Use keyboard shortcuts in PowerPoint. keyboard-shortcuts microsoft-powerpoint share | improve this question edited Aug 14 '14 at 14:49 Linger 2,826 10 28 40
                      Read more

                      How to put 3 figures in Latex with 2 figures side by side and 1 below these side by side images but in...

                      Image
                      1 0 I want to put 3 images in LateX such as 2 figures are side by side horizotally and 3rd figure below these 2 side by side figures but in middle. I have following code: begin{figure}[H] centering begin{minipage}{.5textwidth} centering includegraphics[width=.50linewidth]{Text/Images/Genelec_8010_AP.jpg} captionof{figure}{Genelec 8010 AP} label{fig:Genelec 8010} end{minipage}% begin{minipage}{.5textwidth} centering includegraphics[width=.69linewidth]{Text/Images/Genelec_8020_CPM.jpg} captionof{figure}{Genelec 8020 CPM} label{fig:Genelec 8020} end{minipage}% end{figure} %%Here is my 3rd picture code begin{figure} centering includegraphics[width=5cm]{Text/Images/Genelec_8030_BPM.jpg} caption{Genelec 8030 BPM} label{fig:Genelec 8030} end{figure} I want to ask ho
                      Read more