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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

share|improve this question

asked 51 mins 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 | 

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 51 mins 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 51 mins 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 51 mins 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 51 mins 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 51 mins 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 51 mins 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 28 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
  18 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
  15 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The paper uses different rules.
  $endgroup$
  – Allan Cao
  5 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 30 mins ago

answered 38 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 28 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
  18 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
  15 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The paper uses different rules.
  $endgroup$
  – Allan Cao
  5 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 28 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
  18 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
  15 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The paper uses different rules.
  $endgroup$
  – Allan Cao
  5 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 28 mins ago

Dr XorileDr Xorile

12.9k22569

$endgroup$

share|improve this answer

answered 28 mins ago

Dr XorileDr Xorile

12.9k22569

answered 28 mins ago

Dr XorileDr Xorile

12.9k22569

answered 28 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 30 mins ago

answered 38 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 30 mins ago

answered 38 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 30 mins ago

answered 38 mins ago

simonzacksimonzack

267110

$endgroup$

share|improve this answer

edited 30 mins ago

answered 38 mins ago

simonzacksimonzack

267110

answered 38 mins ago

simonzacksimonzack

267110

answered 38 mins ago

simonzacksimonzack

267110