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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user9888273 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • $begingroup$
    Please clarify: what operations can be used? Addition, subtraction, multiplication, division? Can we concatenate numbers? Etc, etc.
    $endgroup$
    – Hugh
    6 hours ago










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










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










  • $begingroup$
    Possible duplicate of Coppers - Make 24
    $endgroup$
    – North
    18 mins ago










  • $begingroup$
    If I am not mistaken, this question is not asking people to solve the puzzle in question, but is instead asking strategies for how to go about solving it beyond just trying things at random.
    $endgroup$
    – Lunin
    12 secs 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
    6 hours ago










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










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










  • $begingroup$
    Possible duplicate of Coppers - Make 24
    $endgroup$
    – North
    18 mins ago










  • $begingroup$
    If I am not mistaken, this question is not asking people to solve the puzzle in question, but is instead asking strategies for how to go about solving it beyond just trying things at random.
    $endgroup$
    – Lunin
    12 secs 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 3 hours ago









Bass

30k472185




30k472185






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.









asked 6 hours ago









user9888273user9888273

91




91




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.





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.






user9888273 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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
    6 hours ago










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










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










  • $begingroup$
    Possible duplicate of Coppers - Make 24
    $endgroup$
    – North
    18 mins ago










  • $begingroup$
    If I am not mistaken, this question is not asking people to solve the puzzle in question, but is instead asking strategies for how to go about solving it beyond just trying things at random.
    $endgroup$
    – Lunin
    12 secs ago


















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










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










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










  • $begingroup$
    Possible duplicate of Coppers - Make 24
    $endgroup$
    – North
    18 mins ago










  • $begingroup$
    If I am not mistaken, this question is not asking people to solve the puzzle in question, but is instead asking strategies for how to go about solving it beyond just trying things at random.
    $endgroup$
    – Lunin
    12 secs ago
















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




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












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




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












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




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












$begingroup$
Possible duplicate of Coppers - Make 24
$endgroup$
– North
18 mins ago




$begingroup$
Possible duplicate of Coppers - Make 24
$endgroup$
– North
18 mins ago












$begingroup$
If I am not mistaken, this question is not asking people to solve the puzzle in question, but is instead asking strategies for how to go about solving it beyond just trying things at random.
$endgroup$
– Lunin
12 secs ago




$begingroup$
If I am not mistaken, this question is not asking people to solve the puzzle in question, but is instead asking strategies for how to go about solving it beyond just trying things at random.
$endgroup$
– Lunin
12 secs ago










2 Answers
2






active

oldest

votes


















8












$begingroup$

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











$endgroup$





















    1












    $begingroup$

    Here's a fairly simple one:




    $3!times(frac88+3)$







    share|improve this answer









    $endgroup$













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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      8












      $begingroup$

      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











      $endgroup$


















        8












        $begingroup$

        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











        $endgroup$
















          8












          8








          8





          $begingroup$

          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 6 hours ago

























          answered 6 hours ago









          HughHugh

          2,2091925




          2,2091925























              1












              $begingroup$

              Here's a fairly simple one:




              $3!times(frac88+3)$







              share|improve this answer









              $endgroup$


















                1












                $begingroup$

                Here's a fairly simple one:




                $3!times(frac88+3)$







                share|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  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 5 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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