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

Coppers - Make 24$tau$ is greatest! $tau$ is all (from 1 to 20)Largest number with five 1's and five numeric operations90s Number PuzzleHow many consecutive integers can you make using only four digits?Use four 8's to make the number 2016Fix the perfectly ordered equationUse 2, 0, 1 and 8 to make 199Palindromic number puzzle - make 505 from 20202Use 0, 5, 7 and 1 to make 89Use 6, 5 and 3 to make 57

1

$begingroup$

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

edited 2 hours ago

Bass

30k472185

asked 5 hours ago

user9888273user9888273

111

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
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  

add a comment | 

1

$begingroup$

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

edited 2 hours ago

Bass

30k472185

asked 5 hours ago

user9888273user9888273

111

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
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  

add a comment | 

$begingroup$

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

edited 2 hours ago

Bass

30k472185

asked 5 hours ago

user9888273user9888273

111

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.

$endgroup$

share|improve this question

edited 2 hours ago

Bass

30k472185

asked 5 hours ago

user9888273user9888273

111

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

edited 2 hours ago

Bass

30k472185

asked 5 hours ago

user9888273user9888273

111

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.

edited 2 hours ago

Bass

30k472185

edited 2 hours ago

Bass

30k472185

asked 5 hours ago

user9888273user9888273

111

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 5 hours ago

user9888273user9888273

111

2 Answers
2

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7

$begingroup$

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

edited 5 hours ago

answered 5 hours ago

HughHugh

2,1991925

$endgroup$

add a comment | 

1

$begingroup$

Here's a fairly simple one:

$3!times(frac88+3)$

share|improve this answer

answered 4 hours ago

JonMark PerryJonMark Perry

19.3k63991

$endgroup$

add a comment | 

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7

$begingroup$

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

edited 5 hours ago

answered 5 hours ago

HughHugh

2,1991925

$endgroup$

add a comment | 

7

$begingroup$

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

edited 5 hours ago

answered 5 hours ago

HughHugh

2,1991925

$endgroup$

add a comment | 

$begingroup$

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

edited 5 hours ago

answered 5 hours ago

HughHugh

2,1991925

$endgroup$

share|improve this answer

edited 5 hours ago

answered 5 hours ago

HughHugh

2,1991925

answered 5 hours ago

HughHugh

2,1991925

answered 5 hours ago

HughHugh

2,1991925

1

$begingroup$

Here's a fairly simple one:

$3!times(frac88+3)$

share|improve this answer

answered 4 hours ago

JonMark PerryJonMark Perry

19.3k63991

$endgroup$

add a comment | 

1

$begingroup$

Here's a fairly simple one:

$3!times(frac88+3)$

share|improve this answer

answered 4 hours ago

JonMark PerryJonMark Perry

19.3k63991

$endgroup$

add a comment | 

$begingroup$

Here's a fairly simple one:

$3!times(frac88+3)$

share|improve this answer

answered 4 hours ago

JonMark PerryJonMark Perry

19.3k63991

$endgroup$

share|improve this answer

answered 4 hours ago

JonMark PerryJonMark Perry

19.3k63991

answered 4 hours ago

JonMark PerryJonMark Perry

19.3k63991

answered 4 hours ago

JonMark PerryJonMark Perry

19.3k63991