Using only 1s, make 29 with the minimum number of digits
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
asked 56 mins ago
Allan CaoAllan Cao
1063
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$endgroup$
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
asked 56 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
1
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
asked 56 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.
$endgroup$
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
mathematics calculation-puzzle formation-of-numbers
asked 56 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 56 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 56 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 56 mins ago
Allan CaoAllan Cao
1063
asked 56 mins ago
Allan CaoAllan Cao
1063
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.
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.
Allan Cao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
2 Answers
2
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4
$begingroup$
Here's a 7 digits solution:
7 digits: (11-1)x(1+1+1)-1
answered 34 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
23 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
21 mins ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
10 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)
answered 44 mins ago
simonzacksimonzack
267110
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
4
$begingroup$
Here's a 7 digits solution:
7 digits: (11-1)x(1+1+1)-1
answered 34 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
23 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
21 mins ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
10 mins ago
add a comment |
4
$begingroup$
Here's a 7 digits solution:
7 digits: (11-1)x(1+1+1)-1
answered 34 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
23 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
21 mins ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
10 mins ago
add a comment |
4
4
4
$begingroup$
Here's a 7 digits solution:
7 digits: (11-1)x(1+1+1)-1
answered 34 mins ago
Dr XorileDr Xorile
12.9k22569
$endgroup$
Here's a 7 digits solution:
7 digits: (11-1)x(1+1+1)-1
answered 34 mins ago
Dr XorileDr Xorile
12.9k22569
answered 34 mins ago
Dr XorileDr Xorile
12.9k22569
answered 34 mins ago
Dr XorileDr Xorile
12.9k22569
answered 34 mins ago
Dr XorileDr Xorile
12.9k22569
12.9k22569
$begingroup$
That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
$endgroup$
– Allan Cao
23 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
21 mins ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
10 mins ago
add a comment |
$begingroup$
That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
$endgroup$
– Allan Cao
23 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
21 mins ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
10 mins ago
$begingroup$
That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
$endgroup$
– Allan Cao
23 mins ago
$begingroup$
That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
$endgroup$
– Allan Cao
23 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
21 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
21 mins ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
10 mins ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
10 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)
answered 44 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)
answered 44 mins ago
simonzacksimonzack
267110
$endgroup$
add a comment |
2
2
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)
answered 44 mins ago
simonzacksimonzack
267110
$endgroup$
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)
answered 44 mins ago
simonzacksimonzack
267110
edited 36 mins ago
answered 44 mins ago
simonzacksimonzack
267110
answered 44 mins ago
simonzacksimonzack
267110
answered 44 mins ago
simonzacksimonzack
267110
267110
add a comment |
add a comment |
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