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Make 24 using exactly three 3s

Get the largest number using the crazy circuit boardTwo Three-Digit Numbers Added to Make Four-Digit Sum. No Number Can Repeat Itself.Make numbers 1-30 using 2, 0, 1, 9My Three Childrenmake a sum with cardsUse 2, 0, 1 and 8 to make 71Create all numbers from 1-100 by using 1,3,3,71 0 1 0 1 0 1 0 1 0 1Zero, One, Two, Three, etcCross-number of two, three and four-digit numbers

2

$begingroup$

Make 24 using exactly three 3s

Each number formed with a 3 and the 24 in the equation are all base 10.

You cannot introduce any additional digits or constants.

Plus(+), negation/subtraction (-), division(/ or show it with a fraction bar), multiplication(* or use grouping symbols as appropriate), exponentiation(^ or show it with an exponent). regular factorial(!), square root(sqrt(), or the radical symbol), grouping symbols such as parentheses and/or square brackets, and the regular decimal point(not for the repeating decimal) are allowed. No concatenation of any type is allowed.

No other functions/operators are allowed.

I am looking for a total of 10 solutions.

arithmetic number

share|improve this question

edited 2 hours ago

Olive Stemforn

asked 3 hours ago

Olive StemfornOlive Stemforn

495313

$endgroup$

add a comment | 

2

$begingroup$

Make 24 using exactly three 3s

Each number formed with a 3 and the 24 in the equation are all base 10.

You cannot introduce any additional digits or constants.

Plus(+), negation/subtraction (-), division(/ or show it with a fraction bar), multiplication(* or use grouping symbols as appropriate), exponentiation(^ or show it with an exponent). regular factorial(!), square root(sqrt(), or the radical symbol), grouping symbols such as parentheses and/or square brackets, and the regular decimal point(not for the repeating decimal) are allowed. No concatenation of any type is allowed.

No other functions/operators are allowed.

I am looking for a total of 10 solutions.

arithmetic number

share|improve this question

edited 2 hours ago

Olive Stemforn

asked 3 hours ago

Olive StemfornOlive Stemforn

495313

$endgroup$

add a comment | 

$begingroup$

Make 24 using exactly three 3s

Each number formed with a 3 and the 24 in the equation are all base 10.

You cannot introduce any additional digits or constants.

Plus(+), negation/subtraction (-), division(/ or show it with a fraction bar), multiplication(* or use grouping symbols as appropriate), exponentiation(^ or show it with an exponent). regular factorial(!), square root(sqrt(), or the radical symbol), grouping symbols such as parentheses and/or square brackets, and the regular decimal point(not for the repeating decimal) are allowed. No concatenation of any type is allowed.

No other functions/operators are allowed.

I am looking for a total of 10 solutions.

arithmetic number

share|improve this question

edited 2 hours ago

Olive Stemforn

asked 3 hours ago

Olive StemfornOlive Stemforn

495313

$endgroup$

share|improve this question

edited 2 hours ago

Olive Stemforn

asked 3 hours ago

Olive StemfornOlive Stemforn

495313

share|improve this question

edited 2 hours ago

Olive Stemforn

asked 3 hours ago

Olive StemfornOlive Stemforn

495313

asked 3 hours ago

Olive StemfornOlive Stemforn

495313

asked 3 hours ago

Olive StemfornOlive Stemforn

495313

6 Answers
6

active

oldest

votes

5

$begingroup$

Here is my first:

$(3 + frac33)! = 24$

share|improve this answer

edited 3 hours ago

answered 3 hours ago

Weather VaneWeather Vane

3,1131115

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ Weather Vane - Let us say that by adding the square root symbols, you have not changed the values of those. They are redundant. It's similar to writing 1! instead of 1 or 2! instead of 2. Although mathematically correct, I would not see them as "primitive solutions."
  $endgroup$
  – Olive Stemforn
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Ah OK, I was about to add another similar variant - removed.
  $endgroup$
  – Weather Vane
  3 hours ago
  
  

  
  
  
  

add a comment | 

4

$begingroup$

Here is one possible solution:

3*3!+3!

share|improve this answer

answered 3 hours ago

PugmonkeyPugmonkey

3,8001221

$endgroup$

add a comment | 

4

$begingroup$

Solutions

(i) $sqrt3^3! -3 = 24$
(ii) $left(frac3! + 3!3 right)! = 24$
(iii) $ left(frac3.3 - 3! right)! = 24$
(iv) $left(sqrtfrac3.3 + 3! right)! = 24$
(v) $left(3! - frac3!3 right)! = 24$
(vi) $(3*3!)+3! = 24$ (Pugmonkey)
(vii) $(3 + frac33)! = 24$ (Weather Vane)
(viii) $3^3 - 3 = 24$ (Olive)
(ix) $(sqrt3)^3! -3 = 24$ (Rupert)

share|improve this answer

edited 2 hours ago

Rupert Morrish

3,7251935

answered 3 hours ago

hexominohexomino

50.4k4149239

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @WeatherVane Just saw yours.
  $endgroup$
  – hexomino
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yours are prolific.
  $endgroup$
  – Weather Vane
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ hexomino - Please see my note to Weather Vane. Your first three listed are basic/primitive/elegant ones. Keep those.
  $endgroup$
  – Olive Stemforn
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  @JonathanAllan That's what Olive's comment above was referring to.
  $endgroup$
  – hexomino
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @JonathanAllan the similar variant $(3 + fracsqrt3sqrt3)! = 24$ was banned too.
  $endgroup$
  – Weather Vane
  56 mins ago
  

  
  
  
  

 | 
show 7 more comments

1

$begingroup$

$(sqrt3)^3! -3 = 24$

Which is obviously only slightly different to hexomino's:

(i) $sqrt3^3! -3 = 24$

share|improve this answer

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Ah, yes, good spot!
  $endgroup$
  – hexomino
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ Rupert Morrish - Good, your first one listed is a definitely newer type, because, for instance, if the square root symbol were to be dropped, the expression would have a different value.
  $endgroup$
  – Olive Stemforn
  3 hours ago
  

  
  
  
  

add a comment | 

0

$begingroup$

I feel like something should be able to be done with

$frac(3!)!30 = 24$

with judicious use of

decimal points

but I can't find it.

$frac(3!)!3^3 + 3 = 24$

uses 4 3s.

share|improve this answer

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  :: : I will have to leave this computer in about five minutes from now (for up to as long as 20 hours later on) before I post for confirmations of remaining solutions.
  $endgroup$
  – Olive Stemforn
  2 hours ago
  
  

  
  
  
  

add a comment | 

0

$begingroup$

(edit) I will post one of the 10 solutions as an example:

$3^3 - 3 = 24$

share|improve this answer

edited 2 hours ago

Dr Xorile

14.4k33084

answered 3 hours ago

Olive StemfornOlive Stemforn

495313

$endgroup$

add a comment | 

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5

$begingroup$

Here is my first:

$(3 + frac33)! = 24$

share|improve this answer

edited 3 hours ago

answered 3 hours ago

Weather VaneWeather Vane

3,1131115

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ Weather Vane - Let us say that by adding the square root symbols, you have not changed the values of those. They are redundant. It's similar to writing 1! instead of 1 or 2! instead of 2. Although mathematically correct, I would not see them as "primitive solutions."
  $endgroup$
  – Olive Stemforn
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Ah OK, I was about to add another similar variant - removed.
  $endgroup$
  – Weather Vane
  3 hours ago
  
  

  
  
  
  

add a comment | 

5

$begingroup$

Here is my first:

$(3 + frac33)! = 24$

share|improve this answer

edited 3 hours ago

answered 3 hours ago

Weather VaneWeather Vane

3,1131115

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ Weather Vane - Let us say that by adding the square root symbols, you have not changed the values of those. They are redundant. It's similar to writing 1! instead of 1 or 2! instead of 2. Although mathematically correct, I would not see them as "primitive solutions."
  $endgroup$
  – Olive Stemforn
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Ah OK, I was about to add another similar variant - removed.
  $endgroup$
  – Weather Vane
  3 hours ago
  
  

  
  
  
  

add a comment | 

$begingroup$

Here is my first:

$(3 + frac33)! = 24$

share|improve this answer

edited 3 hours ago

answered 3 hours ago

Weather VaneWeather Vane

3,1131115

$endgroup$

share|improve this answer

edited 3 hours ago

answered 3 hours ago

Weather VaneWeather Vane

3,1131115

answered 3 hours ago

Weather VaneWeather Vane

3,1131115

answered 3 hours ago

Weather VaneWeather Vane

3,1131115

4

$begingroup$

Here is one possible solution:

3*3!+3!

share|improve this answer

answered 3 hours ago

PugmonkeyPugmonkey

3,8001221

$endgroup$

add a comment | 

4

$begingroup$

Here is one possible solution:

3*3!+3!

share|improve this answer

answered 3 hours ago

PugmonkeyPugmonkey

3,8001221

$endgroup$

add a comment | 

$begingroup$

Here is one possible solution:

3*3!+3!

share|improve this answer

answered 3 hours ago

PugmonkeyPugmonkey

3,8001221

$endgroup$

share|improve this answer

answered 3 hours ago

PugmonkeyPugmonkey

3,8001221

answered 3 hours ago

PugmonkeyPugmonkey

3,8001221

answered 3 hours ago

PugmonkeyPugmonkey

3,8001221

4

$begingroup$

Solutions

(i) $sqrt3^3! -3 = 24$
(ii) $left(frac3! + 3!3 right)! = 24$
(iii) $ left(frac3.3 - 3! right)! = 24$
(iv) $left(sqrtfrac3.3 + 3! right)! = 24$
(v) $left(3! - frac3!3 right)! = 24$
(vi) $(3*3!)+3! = 24$ (Pugmonkey)
(vii) $(3 + frac33)! = 24$ (Weather Vane)
(viii) $3^3 - 3 = 24$ (Olive)
(ix) $(sqrt3)^3! -3 = 24$ (Rupert)

share|improve this answer

edited 2 hours ago

Rupert Morrish

3,7251935

answered 3 hours ago

hexominohexomino

50.4k4149239

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @WeatherVane Just saw yours.
  $endgroup$
  – hexomino
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yours are prolific.
  $endgroup$
  – Weather Vane
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ hexomino - Please see my note to Weather Vane. Your first three listed are basic/primitive/elegant ones. Keep those.
  $endgroup$
  – Olive Stemforn
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  @JonathanAllan That's what Olive's comment above was referring to.
  $endgroup$
  – hexomino
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @JonathanAllan the similar variant $(3 + fracsqrt3sqrt3)! = 24$ was banned too.
  $endgroup$
  – Weather Vane
  56 mins ago
  

  
  
  
  

 | 
show 7 more comments

4

$begingroup$

Solutions

(i) $sqrt3^3! -3 = 24$
(ii) $left(frac3! + 3!3 right)! = 24$
(iii) $ left(frac3.3 - 3! right)! = 24$
(iv) $left(sqrtfrac3.3 + 3! right)! = 24$
(v) $left(3! - frac3!3 right)! = 24$
(vi) $(3*3!)+3! = 24$ (Pugmonkey)
(vii) $(3 + frac33)! = 24$ (Weather Vane)
(viii) $3^3 - 3 = 24$ (Olive)
(ix) $(sqrt3)^3! -3 = 24$ (Rupert)

share|improve this answer

edited 2 hours ago

Rupert Morrish

3,7251935

answered 3 hours ago

hexominohexomino

50.4k4149239

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @WeatherVane Just saw yours.
  $endgroup$
  – hexomino
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yours are prolific.
  $endgroup$
  – Weather Vane
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ hexomino - Please see my note to Weather Vane. Your first three listed are basic/primitive/elegant ones. Keep those.
  $endgroup$
  – Olive Stemforn
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  @JonathanAllan That's what Olive's comment above was referring to.
  $endgroup$
  – hexomino
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @JonathanAllan the similar variant $(3 + fracsqrt3sqrt3)! = 24$ was banned too.
  $endgroup$
  – Weather Vane
  56 mins ago
  

  
  
  
  

 | 
show 7 more comments

$begingroup$

Solutions

(i) $sqrt3^3! -3 = 24$
(ii) $left(frac3! + 3!3 right)! = 24$
(iii) $ left(frac3.3 - 3! right)! = 24$
(iv) $left(sqrtfrac3.3 + 3! right)! = 24$
(v) $left(3! - frac3!3 right)! = 24$
(vi) $(3*3!)+3! = 24$ (Pugmonkey)
(vii) $(3 + frac33)! = 24$ (Weather Vane)
(viii) $3^3 - 3 = 24$ (Olive)
(ix) $(sqrt3)^3! -3 = 24$ (Rupert)

share|improve this answer

edited 2 hours ago

Rupert Morrish

3,7251935

answered 3 hours ago

hexominohexomino

50.4k4149239

$endgroup$

share|improve this answer

edited 2 hours ago

Rupert Morrish

3,7251935

answered 3 hours ago

hexominohexomino

50.4k4149239

edited 2 hours ago

Rupert Morrish

3,7251935

edited 2 hours ago

Rupert Morrish

3,7251935

answered 3 hours ago

hexominohexomino

50.4k4149239

answered 3 hours ago

hexominohexomino

50.4k4149239

1

$begingroup$

$(sqrt3)^3! -3 = 24$

Which is obviously only slightly different to hexomino's:

(i) $sqrt3^3! -3 = 24$

share|improve this answer

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Ah, yes, good spot!
  $endgroup$
  – hexomino
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ Rupert Morrish - Good, your first one listed is a definitely newer type, because, for instance, if the square root symbol were to be dropped, the expression would have a different value.
  $endgroup$
  – Olive Stemforn
  3 hours ago
  

  
  
  
  

add a comment | 

1

$begingroup$

$(sqrt3)^3! -3 = 24$

Which is obviously only slightly different to hexomino's:

(i) $sqrt3^3! -3 = 24$

share|improve this answer

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Ah, yes, good spot!
  $endgroup$
  – hexomino
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ Rupert Morrish - Good, your first one listed is a definitely newer type, because, for instance, if the square root symbol were to be dropped, the expression would have a different value.
  $endgroup$
  – Olive Stemforn
  3 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

$(sqrt3)^3! -3 = 24$

Which is obviously only slightly different to hexomino's:

(i) $sqrt3^3! -3 = 24$

share|improve this answer

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

$endgroup$

share|improve this answer

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

0

$begingroup$

I feel like something should be able to be done with

$frac(3!)!30 = 24$

with judicious use of

decimal points

but I can't find it.

$frac(3!)!3^3 + 3 = 24$

uses 4 3s.

share|improve this answer

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  :: : I will have to leave this computer in about five minutes from now (for up to as long as 20 hours later on) before I post for confirmations of remaining solutions.
  $endgroup$
  – Olive Stemforn
  2 hours ago
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I feel like something should be able to be done with

$frac(3!)!30 = 24$

with judicious use of

decimal points

but I can't find it.

$frac(3!)!3^3 + 3 = 24$

uses 4 3s.

share|improve this answer

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  :: : I will have to leave this computer in about five minutes from now (for up to as long as 20 hours later on) before I post for confirmations of remaining solutions.
  $endgroup$
  – Olive Stemforn
  2 hours ago
  
  

  
  
  
  

add a comment | 

$begingroup$

I feel like something should be able to be done with

$frac(3!)!30 = 24$

with judicious use of

decimal points

but I can't find it.

$frac(3!)!3^3 + 3 = 24$

uses 4 3s.

share|improve this answer

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

$endgroup$

share|improve this answer

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

answered 3 hours ago

Rupert MorrishRupert Morrish

3,7251935

0

$begingroup$

(edit) I will post one of the 10 solutions as an example:

$3^3 - 3 = 24$

share|improve this answer

edited 2 hours ago

Dr Xorile

14.4k33084

answered 3 hours ago

Olive StemfornOlive Stemforn

495313

$endgroup$

add a comment | 

0

$begingroup$

(edit) I will post one of the 10 solutions as an example:

$3^3 - 3 = 24$

share|improve this answer

edited 2 hours ago

Dr Xorile

14.4k33084

answered 3 hours ago

Olive StemfornOlive Stemforn

495313

$endgroup$

add a comment | 

$begingroup$

(edit) I will post one of the 10 solutions as an example:

$3^3 - 3 = 24$

share|improve this answer

edited 2 hours ago

Dr Xorile

14.4k33084

answered 3 hours ago

Olive StemfornOlive Stemforn

495313

$endgroup$

share|improve this answer

edited 2 hours ago

Dr Xorile

14.4k33084

answered 3 hours ago

Olive StemfornOlive Stemforn

495313

edited 2 hours ago

Dr Xorile

14.4k33084

edited 2 hours ago

Dr Xorile

14.4k33084

answered 3 hours ago

Olive StemfornOlive Stemforn

495313

answered 3 hours ago

Olive StemfornOlive Stemforn

495313