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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
$begingroup$
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 1 hour ago
Allan CaoAllan Cao
1113
New contributor
Allan Cao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$
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
asked 1 hour ago
Allan CaoAllan Cao
1113
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
asked 1 hour ago
Allan CaoAllan Cao
1113
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 1 hour ago
Allan CaoAllan Cao
1113
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
1113
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
1113
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
1113
asked 1 hour ago
Allan CaoAllan Cao
1113
1113
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 |
3 Answers
3
active
oldest
votes
$begingroup$
Here's a 7 digits solution:
7 digits: (11-1)x(1+1+1)-1
answered 1 hour 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
1 hour 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
1 hour ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
52 mins ago
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)
answered 1 hour ago
simonzacksimonzack
267110
$endgroup$
add a comment |
$begingroup$
For the sake of completeness, here's an 8 digit solution:
(1+1+1)^(1+1+1) + 1 + 1
answered 13 mins ago
kwypstonkwypston
1763
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Here's a 7 digits solution:
7 digits: (11-1)x(1+1+1)-1
answered 1 hour 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
1 hour 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
1 hour ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
52 mins ago
add a comment |
$begingroup$
Here's a 7 digits solution:
7 digits: (11-1)x(1+1+1)-1
answered 1 hour 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
1 hour 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
1 hour ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
52 mins ago
add a comment |
$begingroup$
Here's a 7 digits solution:
7 digits: (11-1)x(1+1+1)-1
answered 1 hour ago
Dr XorileDr Xorile
12.9k22569
$endgroup$
Here's a 7 digits solution:
7 digits: (11-1)x(1+1+1)-1
answered 1 hour ago
Dr XorileDr Xorile
12.9k22569
answered 1 hour ago
Dr XorileDr Xorile
12.9k22569
answered 1 hour ago
Dr XorileDr Xorile
12.9k22569
answered 1 hour 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
1 hour 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
1 hour ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
52 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
1 hour 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
1 hour ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
52 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
1 hour 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
1 hour 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
1 hour 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
1 hour ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
52 mins ago
$begingroup$
The paper uses different rules.
$endgroup$
– Allan Cao
52 mins ago
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)
answered 1 hour 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)
answered 1 hour 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)
answered 1 hour 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 1 hour ago
simonzacksimonzack
267110
edited 1 hour ago
answered 1 hour ago
simonzacksimonzack
267110
answered 1 hour ago
simonzacksimonzack
267110
answered 1 hour ago
simonzacksimonzack
267110
267110
add a comment |
add a comment |
$begingroup$
For the sake of completeness, here's an 8 digit solution:
(1+1+1)^(1+1+1) + 1 + 1
answered 13 mins ago
kwypstonkwypston
1763
$endgroup$
add a comment |
$begingroup$
For the sake of completeness, here's an 8 digit solution:
(1+1+1)^(1+1+1) + 1 + 1
answered 13 mins ago
kwypstonkwypston
1763
$endgroup$
add a comment |
$begingroup$
For the sake of completeness, here's an 8 digit solution:
(1+1+1)^(1+1+1) + 1 + 1
answered 13 mins ago
kwypstonkwypston
1763
$endgroup$
For the sake of completeness, here's an 8 digit solution:
(1+1+1)^(1+1+1) + 1 + 1
answered 13 mins ago
kwypstonkwypston
1763
answered 13 mins ago
kwypstonkwypston
1763
answered 13 mins ago
kwypstonkwypston
1763
answered 13 mins ago
kwypstonkwypston
1763
1763
add a comment |
add a comment |
Allan Cao is a new contributor. Be nice, and check out our Code of Conduct.
Allan Cao is a new contributor. Be nice, and check out our Code of Conduct.
Allan Cao is a new contributor. Be nice, and check out our Code of Conduct.
Allan Cao is a new contributor. Be nice, and check out our Code of Conduct.
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