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












2












$begingroup$



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










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










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










  • $begingroup$
    Possible duplicate of Coppers - Make 24
    $endgroup$
    – North
    1 hour 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
    1 hour ago
















2












$begingroup$



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
    7 hours ago










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










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










  • $begingroup$
    Possible duplicate of Coppers - Make 24
    $endgroup$
    – North
    1 hour 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
    1 hour ago














2












2








2





$begingroup$



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 4 hours ago









Bass

30k472185




30k472185






New contributor




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Check out our Code of Conduct.









asked 7 hours ago









user9888273user9888273

191




191




New contributor




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






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
    7 hours ago










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










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










  • $begingroup$
    Possible duplicate of Coppers - Make 24
    $endgroup$
    – North
    1 hour 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
    1 hour ago


















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










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










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










  • $begingroup$
    Possible duplicate of Coppers - Make 24
    $endgroup$
    – North
    1 hour 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
    1 hour ago
















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




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












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




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












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




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












$begingroup$
Possible duplicate of Coppers - Make 24
$endgroup$
– North
1 hour ago




$begingroup$
Possible duplicate of Coppers - Make 24
$endgroup$
– North
1 hour 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
1 hour 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
1 hour ago










3 Answers
3






active

oldest

votes


















11












$begingroup$

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











$endgroup$





















    2












    $begingroup$

    Here's a fairly simple one:




    $3!times(frac88+3)$







    share|improve this answer









    $endgroup$





















      0












      $begingroup$

      enter preformatted text hereStill there are some good answere but this may help you



       8%[3-(8%3)] =24



      8%[3-(8%3)] =24






      share









      $endgroup$













      • $begingroup$
        Any body help me I am still struggling to put a spoiler please edit it
        $endgroup$
        – Purple
        16 mins ago











      Your Answer





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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      11












      $begingroup$

      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











      $endgroup$


















        11












        $begingroup$

        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











        $endgroup$
















          11












          11








          11





          $begingroup$

          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 7 hours ago

























          answered 7 hours ago









          HughHugh

          2,2391926




          2,2391926























              2












              $begingroup$

              Here's a fairly simple one:




              $3!times(frac88+3)$







              share|improve this answer









              $endgroup$


















                2












                $begingroup$

                Here's a fairly simple one:




                $3!times(frac88+3)$







                share|improve this answer









                $endgroup$
















                  2












                  2








                  2





                  $begingroup$

                  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 6 hours ago









                  JonMark PerryJonMark Perry

                  19.3k63991




                  19.3k63991























                      0












                      $begingroup$

                      enter preformatted text hereStill there are some good answere but this may help you



                       8%[3-(8%3)] =24



                      8%[3-(8%3)] =24






                      share









                      $endgroup$













                      • $begingroup$
                        Any body help me I am still struggling to put a spoiler please edit it
                        $endgroup$
                        – Purple
                        16 mins ago
















                      0












                      $begingroup$

                      enter preformatted text hereStill there are some good answere but this may help you



                       8%[3-(8%3)] =24



                      8%[3-(8%3)] =24






                      share









                      $endgroup$













                      • $begingroup$
                        Any body help me I am still struggling to put a spoiler please edit it
                        $endgroup$
                        – Purple
                        16 mins ago














                      0












                      0








                      0





                      $begingroup$

                      enter preformatted text hereStill there are some good answere but this may help you



                       8%[3-(8%3)] =24



                      8%[3-(8%3)] =24






                      share









                      $endgroup$



                      enter preformatted text hereStill there are some good answere but this may help you



                       8%[3-(8%3)] =24



                      8%[3-(8%3)] =24







                      share











                      share


                      share










                      answered 19 mins ago









                      PurplePurple

                      737113




                      737113












                      • $begingroup$
                        Any body help me I am still struggling to put a spoiler please edit it
                        $endgroup$
                        – Purple
                        16 mins ago


















                      • $begingroup$
                        Any body help me I am still struggling to put a spoiler please edit it
                        $endgroup$
                        – Purple
                        16 mins ago
















                      $begingroup$
                      Any body help me I am still struggling to put a spoiler please edit it
                      $endgroup$
                      – Purple
                      16 mins ago




                      $begingroup$
                      Any body help me I am still struggling to put a spoiler please edit it
                      $endgroup$
                      – Purple
                      16 mins ago










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










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                      Tu-95轟炸機

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                      body.skin-minerva .mw-parser-output table.infobox caption{text-align:center} 图-95 Ту–95 北约代号：熊（Bear） 一架在安格斯空军基地的图-95MS 概觀 類型 战略轰炸机 代號 北约代号： Bear （熊） 乘員 7名 駕駛員2名，機尾炮手1名，其他人員4名 首飛 1952年11月12日 服役 1956年 設計 圖波列夫設計局 產量 超过500架 現況 现役 主要用戶   蘇聯   俄羅斯 衍生機型 图-114、图-119、Tu-95 技术数据 長度 49.50米（162呎5吋） 翼展 51.10米（167呎8吋） 高度 12.12米（39呎9吋） 翼面積 310平方米（3,330平方呎） 空重 90,000公斤（198,000磅） 最大起飛重量 188,000公斤（414,500磅） 發動機 4具库兹涅佐夫NK-12MV型渦輪螺旋槳發動機 功率 4×11,000千瓦（14,800馬力） 性能數據 最大速度 925公里／時（500節，575哩／時） 爬升率 10米／秒（2,000呎／分） 最大升限 12,000米（39,000呎） 最大航程 15,000公里（8,100海浬，9,400哩） 翼負荷 606公斤／平方米（124磅／平方呎） 推重比 235 W／公斤（0.143馬力／磅） 武器装备 機炮 1具/2具AM-23型23公釐雷達控制機砲（機尾） 飛彈 空对地导弹： Kh-20、Kh-22 Kh-26、Kh-55 炸彈 60枚FAB-250炸彈，或 30枚FAB-500炸彈。 其他 载弹量（包括飞弹）：最多15,000公斤（33,000磅） Tu-95熊式MR型機 图-95 （俄语： Ту–95 ， 英语： Tu-95 ），北約代號： Bear （ 熊 ），是蘇聯圖波列夫設計局所研製，是全世界唯一服役的大型四渦輪螺旋槳發動機...
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