Use two 8s and two 3s to make the number 24












0












$begingroup$



Use two $8$s, two $3$s, and basic arithmetic operators ($ +, -, times , div$, parentheses) to make the number $24$.



(You may not join numbers together to form new numbers, like $ 8, 3rightarrow 83$)




I don't know how to start besides just trying to find the correct answer. Is there a way you can make this equation through small steps or I should just bruteforce it?






mathematics formation-of-numbers







share|improve this question









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  • $begingroup$
    Please clarify: what operations can be used? Addition, subtraction, multiplication, division? Can we concatenate numbers? Etc, etc.
    $endgroup$
    – Hugh
    3 hours ago










  • $begingroup$
    Also—hasn't this been asked before?
    $endgroup$
    – Hugh
    3 hours ago










  • $begingroup$
    see puzzling.stackexchange.com/questions/50259/coppers-make-24 (GM's answer)
    $endgroup$
    – JonMark Perry
    54 mins ago
















0












$begingroup$



Use two $8$s, two $3$s, and basic arithmetic operators ($ +, -, times , div$, parentheses) to make the number $24$.



(You may not join numbers together to form new numbers, like $ 8, 3rightarrow 83$)




I don't know how to start besides just trying to find the correct answer. Is there a way you can make this equation through small steps or I should just bruteforce it?






mathematics formation-of-numbers







share|improve this question









New contributor




user9888273 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$












  • $begingroup$
    Please clarify: what operations can be used? Addition, subtraction, multiplication, division? Can we concatenate numbers? Etc, etc.
    $endgroup$
    – Hugh
    3 hours ago










  • $begingroup$
    Also—hasn't this been asked before?
    $endgroup$
    – Hugh
    3 hours ago










  • $begingroup$
    see puzzling.stackexchange.com/questions/50259/coppers-make-24 (GM's answer)
    $endgroup$
    – JonMark Perry
    54 mins ago














0












0








0





$begingroup$



Use two $8$s, two $3$s, and basic arithmetic operators ($ +, -, times , div$, parentheses) to make the number $24$.



(You may not join numbers together to form new numbers, like $ 8, 3rightarrow 83$)




I don't know how to start besides just trying to find the correct answer. Is there a way you can make this equation through small steps or I should just bruteforce it?






mathematics formation-of-numbers







share|improve this question









New contributor




user9888273 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$





Use two $8$s, two $3$s, and basic arithmetic operators ($ +, -, times , div$, parentheses) to make the number $24$.



(You may not join numbers together to form new numbers, like $ 8, 3rightarrow 83$)




I don't know how to start besides just trying to find the correct answer. Is there a way you can make this equation through small steps or I should just bruteforce it?






mathematics formation-of-numbers




mathematics formation-of-numbers






share|improve this question









New contributor




user9888273 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




user9888273 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 35 mins ago









Bass

30k472185




30k472185






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asked 3 hours ago









user9888273user9888273

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6




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New contributor





user9888273 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






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Check out our Code of Conduct.












  • $begingroup$
    Please clarify: what operations can be used? Addition, subtraction, multiplication, division? Can we concatenate numbers? Etc, etc.
    $endgroup$
    – Hugh
    3 hours ago










  • $begingroup$
    Also—hasn't this been asked before?
    $endgroup$
    – Hugh
    3 hours ago










  • $begingroup$
    see puzzling.stackexchange.com/questions/50259/coppers-make-24 (GM's answer)
    $endgroup$
    – JonMark Perry
    54 mins ago


















  • $begingroup$
    Please clarify: what operations can be used? Addition, subtraction, multiplication, division? Can we concatenate numbers? Etc, etc.
    $endgroup$
    – Hugh
    3 hours ago










  • $begingroup$
    Also—hasn't this been asked before?
    $endgroup$
    – Hugh
    3 hours ago










  • $begingroup$
    see puzzling.stackexchange.com/questions/50259/coppers-make-24 (GM's answer)
    $endgroup$
    – JonMark Perry
    54 mins ago
















$begingroup$
Please clarify: what operations can be used? Addition, subtraction, multiplication, division? Can we concatenate numbers? Etc, etc.
$endgroup$
– Hugh
3 hours ago




$begingroup$
Please clarify: what operations can be used? Addition, subtraction, multiplication, division? Can we concatenate numbers? Etc, etc.
$endgroup$
– Hugh
3 hours ago












$begingroup$
Also—hasn't this been asked before?
$endgroup$
– Hugh
3 hours ago




$begingroup$
Also—hasn't this been asked before?
$endgroup$
– Hugh
3 hours ago












$begingroup$
see puzzling.stackexchange.com/questions/50259/coppers-make-24 (GM's answer)
$endgroup$
– JonMark Perry
54 mins ago




$begingroup$
see puzzling.stackexchange.com/questions/50259/coppers-make-24 (GM's answer)
$endgroup$
– JonMark Perry
54 mins ago










2 Answers
2






active

oldest

votes


















4












$begingroup$

Here is a solution that uses only "elementary" operations (addition, subtraction, multiplication, and division).




$8 div (3 - (8 div 3))$ (or alternatively $frac{8}{3 - frac{8}{3}}$)
$= 8 div frac{1}{3}$
$= 24$




If we allow square roots, a simpler solution is possible.




$sqrt{8 times 8 times 3 times 3}$
$= 8 times 3$
$= 24$




In fact, there are many more solutions if you allow more operations.






share|improve this answer











$endgroup$





















    0












    $begingroup$

    Here's a fairly simple one:




    $3!times(frac88+3)$







    share|improve this answer









    $endgroup$













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      2 Answers
      2






      active

      oldest

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      2 Answers
      2






      active

      oldest

      votes









      active

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      active

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      4












      $begingroup$

      Here is a solution that uses only "elementary" operations (addition, subtraction, multiplication, and division).




      $8 div (3 - (8 div 3))$ (or alternatively $frac{8}{3 - frac{8}{3}}$)
      $= 8 div frac{1}{3}$
      $= 24$




      If we allow square roots, a simpler solution is possible.




      $sqrt{8 times 8 times 3 times 3}$
      $= 8 times 3$
      $= 24$




      In fact, there are many more solutions if you allow more operations.






      share|improve this answer











      $endgroup$


















        4












        $begingroup$

        Here is a solution that uses only "elementary" operations (addition, subtraction, multiplication, and division).




        $8 div (3 - (8 div 3))$ (or alternatively $frac{8}{3 - frac{8}{3}}$)
        $= 8 div frac{1}{3}$
        $= 24$




        If we allow square roots, a simpler solution is possible.




        $sqrt{8 times 8 times 3 times 3}$
        $= 8 times 3$
        $= 24$




        In fact, there are many more solutions if you allow more operations.






        share|improve this answer











        $endgroup$
















          4












          4








          4





          $begingroup$

          Here is a solution that uses only "elementary" operations (addition, subtraction, multiplication, and division).




          $8 div (3 - (8 div 3))$ (or alternatively $frac{8}{3 - frac{8}{3}}$)
          $= 8 div frac{1}{3}$
          $= 24$




          If we allow square roots, a simpler solution is possible.




          $sqrt{8 times 8 times 3 times 3}$
          $= 8 times 3$
          $= 24$




          In fact, there are many more solutions if you allow more operations.






          share|improve this answer











          $endgroup$



          Here is a solution that uses only "elementary" operations (addition, subtraction, multiplication, and division).




          $8 div (3 - (8 div 3))$ (or alternatively $frac{8}{3 - frac{8}{3}}$)
          $= 8 div frac{1}{3}$
          $= 24$




          If we allow square roots, a simpler solution is possible.




          $sqrt{8 times 8 times 3 times 3}$
          $= 8 times 3$
          $= 24$




          In fact, there are many more solutions if you allow more operations.







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 3 hours ago

























          answered 3 hours ago









          HughHugh

          2,1691925




          2,1691925























              0












              $begingroup$

              Here's a fairly simple one:




              $3!times(frac88+3)$







              share|improve this answer









              $endgroup$


















                0












                $begingroup$

                Here's a fairly simple one:




                $3!times(frac88+3)$







                share|improve this answer









                $endgroup$
















                  0












                  0








                  0





                  $begingroup$

                  Here's a fairly simple one:




                  $3!times(frac88+3)$







                  share|improve this answer









                  $endgroup$



                  Here's a fairly simple one:




                  $3!times(frac88+3)$








                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 2 hours ago









                  JonMark PerryJonMark Perry

                  19.3k63991




                  19.3k63991






















                      user9888273 is a new contributor. Be nice, and check out our Code of Conduct.










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