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Using only 1s, make 29 with the minimum number of digits

Making π from 1 2 3 4 5 6 7 8 9Express the number $2015$ using only the digit $2$ twiceHow many consecutive positive integers can you make using exactly four instances of the digit '4'?Make numbers 1 - 32 using the digits 2, 0, 1, 7Most consecutive positive integers using two 1sMake numbers 1-31 with 1,9,7,8Make numbers 1 - 30 using the digits 2, 0, 1, 8Make numbers 93 using the digits 2, 0, 1, 8Make numbers 33-100 using only digits 2,0,1,8Make numbers 1-30 using 2, 0, 1, 9

1

$begingroup$

Operations permitted:

• Standard operations: +, −, ×, ÷


• Negation: −


• Exponentiation of two numbers: x^y


• Square root of a number: √


• Factorial: !


• Concatenation of the original digits: dd

mathematics calculation-puzzle formation-of-numbers

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asked 1 hour ago

Allan CaoAllan Cao

1063

New contributor

Allan Cao 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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add a comment | 

1

$begingroup$

Operations permitted:

• Standard operations: +, −, ×, ÷


• Negation: −


• Exponentiation of two numbers: x^y


• Square root of a number: √


• Factorial: !


• Concatenation of the original digits: dd

mathematics calculation-puzzle formation-of-numbers

share|improve this question

asked 1 hour ago

Allan CaoAllan Cao

1063

New contributor

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

$endgroup$

add a comment | 

$begingroup$

Operations permitted:

• Standard operations: +, −, ×, ÷


• Negation: −


• Exponentiation of two numbers: x^y


• Square root of a number: √


• Factorial: !


• Concatenation of the original digits: dd

mathematics calculation-puzzle formation-of-numbers

share|improve this question

asked 1 hour ago

Allan CaoAllan Cao

1063

New contributor

Allan Cao 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

asked 1 hour ago

Allan CaoAllan Cao

1063

New contributor

Allan Cao 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

asked 1 hour ago

Allan CaoAllan Cao

1063

New contributor

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

asked 1 hour ago

Allan CaoAllan Cao

1063

New contributor

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

asked 1 hour ago

Allan CaoAllan Cao

1063

2 Answers
2

active

oldest

votes

4

$begingroup$

Here's a 7 digits solution:

7 digits: (11-1)x(1+1+1)-1

share|improve this answer

answered 41 mins ago

Dr XorileDr Xorile

12.9k22569

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
  $endgroup$
  – Allan Cao
  31 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Do you mean that allowing concatenations should reduce it from 7 to 6? Or are the constraints the same in the paper you cite as in the question above?
  $endgroup$
  – Dr Xorile
  28 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The paper uses different rules.
  $endgroup$
  – Allan Cao
  18 mins ago
  

  
  
  
  

add a comment | 

2

$begingroup$

Lowest I managed so far is 9 digits:

(1 + 1 + 1 + 1)! + 1 + 1 + 1 + 1 + 1

11*(1 + 1 + 1) - (1 + 1 + 1 + 1)

Some other ways I came up with:

(1 + 1)^(1 + 1 + 1 + 1 + 1) - 1 - 1 - 1 (10 digits)

(1 + 1 + 1 + 1 + 1)!/(1 + 1 + 1 + 1) - 1 (10 digits)

(1 + 1 + 1 + 1 + 1)^(1 + 1) + 1 + 1 + 1 + 1 (11 digits)

11*(1 + 1) + 1 + 1 + 1 + 1 + 1 + 1 + 1 (11 digits)

share|improve this answer

edited 43 mins ago

answered 51 mins ago

simonzacksimonzack

267110

$endgroup$

add a comment | 

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4

$begingroup$

Here's a 7 digits solution:

7 digits: (11-1)x(1+1+1)-1

share|improve this answer

answered 41 mins ago

Dr XorileDr Xorile

12.9k22569

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
  $endgroup$
  – Allan Cao
  31 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Do you mean that allowing concatenations should reduce it from 7 to 6? Or are the constraints the same in the paper you cite as in the question above?
  $endgroup$
  – Dr Xorile
  28 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The paper uses different rules.
  $endgroup$
  – Allan Cao
  18 mins ago
  

  
  
  
  

add a comment | 

4

$begingroup$

Here's a 7 digits solution:

7 digits: (11-1)x(1+1+1)-1

share|improve this answer

answered 41 mins ago

Dr XorileDr Xorile

12.9k22569

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
  $endgroup$
  – Allan Cao
  31 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Do you mean that allowing concatenations should reduce it from 7 to 6? Or are the constraints the same in the paper you cite as in the question above?
  $endgroup$
  – Dr Xorile
  28 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The paper uses different rules.
  $endgroup$
  – Allan Cao
  18 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

Here's a 7 digits solution:

7 digits: (11-1)x(1+1+1)-1

share|improve this answer

answered 41 mins ago

Dr XorileDr Xorile

12.9k22569

$endgroup$

share|improve this answer

answered 41 mins ago

Dr XorileDr Xorile

12.9k22569

answered 41 mins ago

Dr XorileDr Xorile

12.9k22569

answered 41 mins ago

Dr XorileDr Xorile

12.9k22569

2

$begingroup$

Lowest I managed so far is 9 digits:

(1 + 1 + 1 + 1)! + 1 + 1 + 1 + 1 + 1

11*(1 + 1 + 1) - (1 + 1 + 1 + 1)

Some other ways I came up with:

(1 + 1)^(1 + 1 + 1 + 1 + 1) - 1 - 1 - 1 (10 digits)

(1 + 1 + 1 + 1 + 1)!/(1 + 1 + 1 + 1) - 1 (10 digits)

(1 + 1 + 1 + 1 + 1)^(1 + 1) + 1 + 1 + 1 + 1 (11 digits)

11*(1 + 1) + 1 + 1 + 1 + 1 + 1 + 1 + 1 (11 digits)

share|improve this answer

edited 43 mins ago

answered 51 mins ago

simonzacksimonzack

267110

$endgroup$

add a comment | 

2

$begingroup$

Lowest I managed so far is 9 digits:

(1 + 1 + 1 + 1)! + 1 + 1 + 1 + 1 + 1

11*(1 + 1 + 1) - (1 + 1 + 1 + 1)

Some other ways I came up with:

(1 + 1)^(1 + 1 + 1 + 1 + 1) - 1 - 1 - 1 (10 digits)

(1 + 1 + 1 + 1 + 1)!/(1 + 1 + 1 + 1) - 1 (10 digits)

(1 + 1 + 1 + 1 + 1)^(1 + 1) + 1 + 1 + 1 + 1 (11 digits)

11*(1 + 1) + 1 + 1 + 1 + 1 + 1 + 1 + 1 (11 digits)

share|improve this answer

edited 43 mins ago

answered 51 mins ago

simonzacksimonzack

267110

$endgroup$

add a comment | 

$begingroup$

Lowest I managed so far is 9 digits:

(1 + 1 + 1 + 1)! + 1 + 1 + 1 + 1 + 1

11*(1 + 1 + 1) - (1 + 1 + 1 + 1)

Some other ways I came up with:

(1 + 1)^(1 + 1 + 1 + 1 + 1) - 1 - 1 - 1 (10 digits)

(1 + 1 + 1 + 1 + 1)!/(1 + 1 + 1 + 1) - 1 (10 digits)

(1 + 1 + 1 + 1 + 1)^(1 + 1) + 1 + 1 + 1 + 1 (11 digits)

11*(1 + 1) + 1 + 1 + 1 + 1 + 1 + 1 + 1 (11 digits)

share|improve this answer

edited 43 mins ago

answered 51 mins ago

simonzacksimonzack

267110

$endgroup$

share|improve this answer

edited 43 mins ago

answered 51 mins ago

simonzacksimonzack

267110

answered 51 mins ago

simonzacksimonzack

267110

answered 51 mins ago

simonzacksimonzack

267110