Code Golf

#18: Post edited by

trichoplax‭ · 2023-10-07T23:08:03Z (about 1 year ago)
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~~Borromean coprimes~~

Borromean coprimes [FINALIZED]

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "True" and "False".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `False`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `False`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `True`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
Here is some Python code that meets the requirements of this challenge. The function `borromean_coprimes` returns `True` or `False`.
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(x, y):
return gcd(x, y) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : "output"`.
You may use any 2 distinct values instead of "True" and "False".
```text
1, 1, 1 : "False"
1, 1, 2 : "False"
1, 1, 3 : "False"
1, 2, 2 : "False"
1, 2, 3 : "False"
2, 2, 2 : "False"
2, 2, 3 : "False"
2, 3, 3 : "False"
2, 3, 4 : "False"
2, 3, 5 : "False"
2, 4, 5 : "False"
2, 4, 6 : "False"
127, 127, 127: "False"
18, 33, 88 : "True"
108, 20, 105 : "True"
98, 30, 105 : "True"
22, 36, 33 : "True"
82, 30, 123 : "True"
40, 55, 22 : "True"
45, 12, 10 : "True"
38, 57, 78 : "True"
35, 84, 80 : "True"
84, 33, 22 : "True"
105, 54, 80 : "True"
26, 96, 39 : "True"
18, 26, 117 : "True"
50, 75, 48 : "True"
95, 76, 70 : "True"
50, 96, 45 : "True"
85, 34, 40 : "True"
84, 104, 39 : "True"
45, 72, 110 : "True"
72, 68, 51 : "True"
20, 105, 28 : "True"
75, 102, 100 : "True"
90, 105, 14 : "True"
105, 110, 84 : "True"
78, 70, 21 : "True"
105, 96, 14 : "True"
110, 120, 33 : "True"
70, 84, 15 : "True"
50, 6, 105 : "True"
70, 21, 45 : "True"
48, 70, 21 : "True"
76, 18, 57 : "True"
126, 77, 66 : "True"
6, 88, 99 : "True"
33, 77, 126 : "True"
88, 72, 33 : "True"
12, 63, 56 : "True"
80, 36, 105 : "True"
35, 110, 77 : "True"
21, 14, 18 : "True"
68, 85, 70 : "True"
75, 108, 80 : "True"
18, 21, 98 : "True"
26, 36, 39 : "True"
30, 98, 21 : "True"
50, 15, 36 : "True"
78, 51, 34 : "True"
44, 98, 77 : "True"
114, 105, 80 : "True"
15, 10, 72 : "True"
5, 91, 18 : "False"
51, 41, 98 : "False"
66, 78, 20 : "False"
76, 18, 50 : "False"
124, 105, 50 : "False"
54, 1, 93 : "False"
60, 41, 104 : "False"
127, 62, 40 : "False"
112, 101, 122 : "False"
7, 12, 74 : "False"
18, 95, 71 : "False"
123, 74, 3 : "False"
51, 79, 7 : "False"
9, 67, 98 : "False"
37, 6, 90 : "False"
43, 1, 45 : "False"
36, 14, 44 : "False"
37, 1, 111 : "False"
55, 89, 26 : "False"
90, 53, 28 : "False"
83, 12, 31 : "False"
19, 112, 5 : "False"
92, 19, 99 : "False"
58, 59, 124 : "False"
9, 106, 85 : "False"
108, 108, 6 : "False"
69, 31, 76 : "False"
96, 6, 42 : "False"
105, 47, 90 : "False"
43, 22, 29 : "False"
113, 19, 73 : "False"
77, 103, 113 : "False"
91, 89, 17 : "False"
60, 16, 61 : "False"
44, 87, 115 : "False"
28, 80, 108 : "False"
11, 116, 76 : "False"
105, 79, 95 : "False"
62, 80, 80 : "False"
7, 60, 104 : "False"
91, 106, 34 : "False"
125, 105, 56 : "False"
9, 74, 87 : "False"
88, 68, 6 : "False"
40, 17, 109 : "False"
116, 83, 29 : "False"
102, 32, 110 : "False"
121, 20, 85 : "False"
112, 44, 121 : "False"
74, 102, 39 : "False"
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

# Now posted: [Borromean coprimes](https://codegolf.codidact.com/posts/289921)
---
Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "True" and "False".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `False`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `False`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `True`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
Here is some Python code that meets the requirements of this challenge. The function `borromean_coprimes` returns `True` or `False`.
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(x, y):
return gcd(x, y) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : "output"`.
You may use any 2 distinct values instead of "True" and "False".
```text
1, 1, 1 : "False"
1, 1, 2 : "False"
1, 1, 3 : "False"
1, 2, 2 : "False"
1, 2, 3 : "False"
2, 2, 2 : "False"
2, 2, 3 : "False"
2, 3, 3 : "False"
2, 3, 4 : "False"
2, 3, 5 : "False"
2, 4, 5 : "False"
2, 4, 6 : "False"
127, 127, 127: "False"
18, 33, 88 : "True"
108, 20, 105 : "True"
98, 30, 105 : "True"
22, 36, 33 : "True"
82, 30, 123 : "True"
40, 55, 22 : "True"
45, 12, 10 : "True"
38, 57, 78 : "True"
35, 84, 80 : "True"
84, 33, 22 : "True"
105, 54, 80 : "True"
26, 96, 39 : "True"
18, 26, 117 : "True"
50, 75, 48 : "True"
95, 76, 70 : "True"
50, 96, 45 : "True"
85, 34, 40 : "True"
84, 104, 39 : "True"
45, 72, 110 : "True"
72, 68, 51 : "True"
20, 105, 28 : "True"
75, 102, 100 : "True"
90, 105, 14 : "True"
105, 110, 84 : "True"
78, 70, 21 : "True"
105, 96, 14 : "True"
110, 120, 33 : "True"
70, 84, 15 : "True"
50, 6, 105 : "True"
70, 21, 45 : "True"
48, 70, 21 : "True"
76, 18, 57 : "True"
126, 77, 66 : "True"
6, 88, 99 : "True"
33, 77, 126 : "True"
88, 72, 33 : "True"
12, 63, 56 : "True"
80, 36, 105 : "True"
35, 110, 77 : "True"
21, 14, 18 : "True"
68, 85, 70 : "True"
75, 108, 80 : "True"
18, 21, 98 : "True"
26, 36, 39 : "True"
30, 98, 21 : "True"
50, 15, 36 : "True"
78, 51, 34 : "True"
44, 98, 77 : "True"
114, 105, 80 : "True"
15, 10, 72 : "True"
5, 91, 18 : "False"
51, 41, 98 : "False"
66, 78, 20 : "False"
76, 18, 50 : "False"
124, 105, 50 : "False"
54, 1, 93 : "False"
60, 41, 104 : "False"
127, 62, 40 : "False"
112, 101, 122 : "False"
7, 12, 74 : "False"
18, 95, 71 : "False"
123, 74, 3 : "False"
51, 79, 7 : "False"
9, 67, 98 : "False"
37, 6, 90 : "False"
43, 1, 45 : "False"
36, 14, 44 : "False"
37, 1, 111 : "False"
55, 89, 26 : "False"
90, 53, 28 : "False"
83, 12, 31 : "False"
19, 112, 5 : "False"
92, 19, 99 : "False"
58, 59, 124 : "False"
9, 106, 85 : "False"
108, 108, 6 : "False"
69, 31, 76 : "False"
96, 6, 42 : "False"
105, 47, 90 : "False"
43, 22, 29 : "False"
113, 19, 73 : "False"
77, 103, 113 : "False"
91, 89, 17 : "False"
60, 16, 61 : "False"
44, 87, 115 : "False"
28, 80, 108 : "False"
11, 116, 76 : "False"
105, 79, 95 : "False"
62, 80, 80 : "False"
7, 60, 104 : "False"
91, 106, 34 : "False"
125, 105, 56 : "False"
9, 74, 87 : "False"
88, 68, 6 : "False"
40, 17, 109 : "False"
116, 83, 29 : "False"
102, 32, 110 : "False"
121, 20, 85 : "False"
112, 44, 121 : "False"
74, 102, 39 : "False"
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

code-golf math

code-golf math finalized

#17: Post edited by

trichoplax‭ · 2023-10-07T23:04:56Z (about 1 year ago)
Make outputs consistently title case

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
~~- 1 of 2 distinct values to represent "true" and "false".~~
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
~~- Output: `false`~~
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
~~- Output: `false`~~
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
~~- Output: `true`~~
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
Here is some Python code that meets the requirements of this challenge. The function `borromean_coprimes` returns `True` or `False`.
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(x, y):
return gcd(x, y) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : "output"`.
You may use any 2 distinct values instead of "True" and "False".
```text
1, 1, 1 : "False"
1, 1, 2 : "False"
1, 1, 3 : "False"
1, 2, 2 : "False"
1, 2, 3 : "False"
2, 2, 2 : "False"
2, 2, 3 : "False"
2, 3, 3 : "False"
2, 3, 4 : "False"
2, 3, 5 : "False"
2, 4, 5 : "False"
2, 4, 6 : "False"
127, 127, 127: "False"
18, 33, 88 : "True"
108, 20, 105 : "True"
98, 30, 105 : "True"
22, 36, 33 : "True"
82, 30, 123 : "True"
40, 55, 22 : "True"
45, 12, 10 : "True"
38, 57, 78 : "True"
35, 84, 80 : "True"
84, 33, 22 : "True"
105, 54, 80 : "True"
26, 96, 39 : "True"
18, 26, 117 : "True"
50, 75, 48 : "True"
95, 76, 70 : "True"
50, 96, 45 : "True"
85, 34, 40 : "True"
84, 104, 39 : "True"
45, 72, 110 : "True"
72, 68, 51 : "True"
20, 105, 28 : "True"
75, 102, 100 : "True"
90, 105, 14 : "True"
105, 110, 84 : "True"
78, 70, 21 : "True"
105, 96, 14 : "True"
110, 120, 33 : "True"
70, 84, 15 : "True"
50, 6, 105 : "True"
70, 21, 45 : "True"
48, 70, 21 : "True"
76, 18, 57 : "True"
126, 77, 66 : "True"
6, 88, 99 : "True"
33, 77, 126 : "True"
88, 72, 33 : "True"
12, 63, 56 : "True"
80, 36, 105 : "True"
35, 110, 77 : "True"
21, 14, 18 : "True"
68, 85, 70 : "True"
75, 108, 80 : "True"
18, 21, 98 : "True"
26, 36, 39 : "True"
30, 98, 21 : "True"
50, 15, 36 : "True"
78, 51, 34 : "True"
44, 98, 77 : "True"
114, 105, 80 : "True"
15, 10, 72 : "True"
5, 91, 18 : "False"
51, 41, 98 : "False"
66, 78, 20 : "False"
76, 18, 50 : "False"
124, 105, 50 : "False"
54, 1, 93 : "False"
60, 41, 104 : "False"
127, 62, 40 : "False"
112, 101, 122 : "False"
7, 12, 74 : "False"
18, 95, 71 : "False"
123, 74, 3 : "False"
51, 79, 7 : "False"
9, 67, 98 : "False"
37, 6, 90 : "False"
43, 1, 45 : "False"
36, 14, 44 : "False"
37, 1, 111 : "False"
55, 89, 26 : "False"
90, 53, 28 : "False"
83, 12, 31 : "False"
19, 112, 5 : "False"
92, 19, 99 : "False"
58, 59, 124 : "False"
9, 106, 85 : "False"
108, 108, 6 : "False"
69, 31, 76 : "False"
96, 6, 42 : "False"
105, 47, 90 : "False"
43, 22, 29 : "False"
113, 19, 73 : "False"
77, 103, 113 : "False"
91, 89, 17 : "False"
60, 16, 61 : "False"
44, 87, 115 : "False"
28, 80, 108 : "False"
11, 116, 76 : "False"
105, 79, 95 : "False"
62, 80, 80 : "False"
7, 60, 104 : "False"
91, 106, 34 : "False"
125, 105, 56 : "False"
9, 74, 87 : "False"
88, 68, 6 : "False"
40, 17, 109 : "False"
116, 83, 29 : "False"
102, 32, 110 : "False"
121, 20, 85 : "False"
112, 44, 121 : "False"
74, 102, 39 : "False"
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "True" and "False".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `False`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `False`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `True`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
Here is some Python code that meets the requirements of this challenge. The function `borromean_coprimes` returns `True` or `False`.
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(x, y):
return gcd(x, y) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : "output"`.
You may use any 2 distinct values instead of "True" and "False".
```text
1, 1, 1 : "False"
1, 1, 2 : "False"
1, 1, 3 : "False"
1, 2, 2 : "False"
1, 2, 3 : "False"
2, 2, 2 : "False"
2, 2, 3 : "False"
2, 3, 3 : "False"
2, 3, 4 : "False"
2, 3, 5 : "False"
2, 4, 5 : "False"
2, 4, 6 : "False"
127, 127, 127: "False"
18, 33, 88 : "True"
108, 20, 105 : "True"
98, 30, 105 : "True"
22, 36, 33 : "True"
82, 30, 123 : "True"
40, 55, 22 : "True"
45, 12, 10 : "True"
38, 57, 78 : "True"
35, 84, 80 : "True"
84, 33, 22 : "True"
105, 54, 80 : "True"
26, 96, 39 : "True"
18, 26, 117 : "True"
50, 75, 48 : "True"
95, 76, 70 : "True"
50, 96, 45 : "True"
85, 34, 40 : "True"
84, 104, 39 : "True"
45, 72, 110 : "True"
72, 68, 51 : "True"
20, 105, 28 : "True"
75, 102, 100 : "True"
90, 105, 14 : "True"
105, 110, 84 : "True"
78, 70, 21 : "True"
105, 96, 14 : "True"
110, 120, 33 : "True"
70, 84, 15 : "True"
50, 6, 105 : "True"
70, 21, 45 : "True"
48, 70, 21 : "True"
76, 18, 57 : "True"
126, 77, 66 : "True"
6, 88, 99 : "True"
33, 77, 126 : "True"
88, 72, 33 : "True"
12, 63, 56 : "True"
80, 36, 105 : "True"
35, 110, 77 : "True"
21, 14, 18 : "True"
68, 85, 70 : "True"
75, 108, 80 : "True"
18, 21, 98 : "True"
26, 36, 39 : "True"
30, 98, 21 : "True"
50, 15, 36 : "True"
78, 51, 34 : "True"
44, 98, 77 : "True"
114, 105, 80 : "True"
15, 10, 72 : "True"
5, 91, 18 : "False"
51, 41, 98 : "False"
66, 78, 20 : "False"
76, 18, 50 : "False"
124, 105, 50 : "False"
54, 1, 93 : "False"
60, 41, 104 : "False"
127, 62, 40 : "False"
112, 101, 122 : "False"
7, 12, 74 : "False"
18, 95, 71 : "False"
123, 74, 3 : "False"
51, 79, 7 : "False"
9, 67, 98 : "False"
37, 6, 90 : "False"
43, 1, 45 : "False"
36, 14, 44 : "False"
37, 1, 111 : "False"
55, 89, 26 : "False"
90, 53, 28 : "False"
83, 12, 31 : "False"
19, 112, 5 : "False"
92, 19, 99 : "False"
58, 59, 124 : "False"
9, 106, 85 : "False"
108, 108, 6 : "False"
69, 31, 76 : "False"
96, 6, 42 : "False"
105, 47, 90 : "False"
43, 22, 29 : "False"
113, 19, 73 : "False"
77, 103, 113 : "False"
91, 89, 17 : "False"
60, 16, 61 : "False"
44, 87, 115 : "False"
28, 80, 108 : "False"
11, 116, 76 : "False"
105, 79, 95 : "False"
62, 80, 80 : "False"
7, 60, 104 : "False"
91, 106, 34 : "False"
125, 105, 56 : "False"
9, 74, 87 : "False"
88, 68, 6 : "False"
40, 17, 109 : "False"
116, 83, 29 : "False"
102, 32, 110 : "False"
121, 20, 85 : "False"
112, 44, 121 : "False"
74, 102, 39 : "False"
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#16: Post edited by

trichoplax‭ · 2023-10-07T23:02:00Z (about 1 year ago)
Add randomly generated test cases including inputs up to and including 127

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
Here is some Python code that meets the requirements of this challenge. The function `borromean_coprimes` returns `True` or `False`.
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(x, y):
return gcd(x, y) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
~~Test cases are in the format `comma, separated, inputs : output`.~~
~~You may use any 2 distinct values instead of "true" and "false".~~
```text
~~1, 1, 1 : false~~
~~1, 1, 2 : false~~
~~1, 1, 3 : false~~
~~1, 2, 2 : false~~
~~1, 2, 3 : false~~
~~2, 2, 2 : false~~
~~2, 2, 3 : false~~
~~2, 3, 3 : false~~
~~2, 3, 4 : false~~
~~2, 3, 5 : false~~
~~2, 4, 5 : false~~
~~2, 4, 6 : false~~
~~6, 10, 15 : true~~
~~6, 15, 10 : true~~
~~10, 6, 15 : true~~
~~10, 15, 6 : true~~
~~15, 6, 10 : true~~
~~15, 10, 6 : true~~
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
~~42, 105, 70 : false~~
70, 42, 105 : false
~~70, 105, 42 : false~~
~~105, 42, 70 : false~~
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
~~30, 14, 105 : true~~
30, 105, 14 : true
~~105, 14, 30 : true~~
~~105, 30, 14 : true~~
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
Here is some Python code that meets the requirements of this challenge. The function `borromean_coprimes` returns `True` or `False`.
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(x, y):
return gcd(x, y) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : "output"`.
You may use any 2 distinct values instead of "True" and "False".
```text
1, 1, 1 : "False"
1, 1, 2 : "False"
1, 1, 3 : "False"
1, 2, 2 : "False"
1, 2, 3 : "False"
2, 2, 2 : "False"
2, 2, 3 : "False"
2, 3, 3 : "False"
2, 3, 4 : "False"
2, 3, 5 : "False"
2, 4, 5 : "False"
2, 4, 6 : "False"
127, 127, 127: "False"
18, 33, 88 : "True"
108, 20, 105 : "True"
98, 30, 105 : "True"
22, 36, 33 : "True"
82, 30, 123 : "True"
40, 55, 22 : "True"
45, 12, 10 : "True"
38, 57, 78 : "True"
35, 84, 80 : "True"
84, 33, 22 : "True"
105, 54, 80 : "True"
26, 96, 39 : "True"
18, 26, 117 : "True"
50, 75, 48 : "True"
95, 76, 70 : "True"
50, 96, 45 : "True"
85, 34, 40 : "True"
84, 104, 39 : "True"
45, 72, 110 : "True"
72, 68, 51 : "True"
20, 105, 28 : "True"
75, 102, 100 : "True"
90, 105, 14 : "True"
105, 110, 84 : "True"
78, 70, 21 : "True"
105, 96, 14 : "True"
110, 120, 33 : "True"
70, 84, 15 : "True"
50, 6, 105 : "True"
70, 21, 45 : "True"
48, 70, 21 : "True"
76, 18, 57 : "True"
126, 77, 66 : "True"
6, 88, 99 : "True"
33, 77, 126 : "True"
88, 72, 33 : "True"
12, 63, 56 : "True"
80, 36, 105 : "True"
35, 110, 77 : "True"
21, 14, 18 : "True"
68, 85, 70 : "True"
75, 108, 80 : "True"
18, 21, 98 : "True"
26, 36, 39 : "True"
30, 98, 21 : "True"
50, 15, 36 : "True"
78, 51, 34 : "True"
44, 98, 77 : "True"
114, 105, 80 : "True"
15, 10, 72 : "True"
5, 91, 18 : "False"
51, 41, 98 : "False"
66, 78, 20 : "False"
76, 18, 50 : "False"
124, 105, 50 : "False"
54, 1, 93 : "False"
60, 41, 104 : "False"
127, 62, 40 : "False"
112, 101, 122 : "False"
7, 12, 74 : "False"
18, 95, 71 : "False"
123, 74, 3 : "False"
51, 79, 7 : "False"
9, 67, 98 : "False"
37, 6, 90 : "False"
43, 1, 45 : "False"
36, 14, 44 : "False"
37, 1, 111 : "False"
55, 89, 26 : "False"
90, 53, 28 : "False"
83, 12, 31 : "False"
19, 112, 5 : "False"
92, 19, 99 : "False"
58, 59, 124 : "False"
9, 106, 85 : "False"
108, 108, 6 : "False"
69, 31, 76 : "False"
96, 6, 42 : "False"
105, 47, 90 : "False"
43, 22, 29 : "False"
113, 19, 73 : "False"
77, 103, 113 : "False"
91, 89, 17 : "False"
60, 16, 61 : "False"
44, 87, 115 : "False"
28, 80, 108 : "False"
11, 116, 76 : "False"
105, 79, 95 : "False"
62, 80, 80 : "False"
7, 60, 104 : "False"
91, 106, 34 : "False"
125, 105, 56 : "False"
9, 74, 87 : "False"
88, 68, 6 : "False"
40, 17, 109 : "False"
116, 83, 29 : "False"
102, 32, 110 : "False"
121, 20, 85 : "False"
112, 44, 121 : "False"
74, 102, 39 : "False"
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#15: Post edited by

trichoplax‭ · 2023-10-04T13:36:26Z (about 1 year ago)
Make parameter names consistent

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
Here is some Python code that meets the requirements of this challenge. The function `borromean_coprimes` returns `True` or `False`.
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
~~def coprime(a, b):~~
~~return gcd(a, b) == 1~~
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
Here is some Python code that meets the requirements of this challenge. The function `borromean_coprimes` returns `True` or `False`.
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(x, y):
return gcd(x, y) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#14: Post edited by

trichoplax‭ · 2023-10-04T06:36:20Z (about 1 year ago)
Mention example code is in Python

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(a, b):
return gcd(a, b) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
Here is some Python code that meets the requirements of this challenge. The function `borromean_coprimes` returns `True` or `False`.
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(a, b):
return gcd(a, b) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#13: Post edited by

trichoplax‭ · 2023-10-03T19:46:35Z (about 1 year ago)
Add syntax highlighting

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
```text
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(a, b):
return gcd(a, b) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
```python
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(a, b):
return gcd(a, b) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#12: Post edited by

trichoplax‭ · 2023-10-03T19:41:51Z (about 1 year ago)
Add non-golfed example code

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
```text
~~To be added, probably in Python~~
~~unless there's a preference~~
~~for something else.~~
```
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
```text
from math import gcd
def borromean_coprimes(x, y, z):
return (
coprime_triple(x, y, z)
and not coprime(x, y)
and not coprime(x, z)
and not coprime(y, z)
)
def coprime(a, b):
return gcd(a, b) == 1
def coprime_triple(x, y, z):
return gcd(x, y, z) == 1
```
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#11: Post edited by

trichoplax‭ · 2023-10-03T18:58:18Z (about 1 year ago)
Placeholder for non-golfed example implementation

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Non-golfed example code
```text
To be added, probably in Python
unless there's a preference
for something else.
```
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#10: Post edited by

trichoplax‭ · 2023-10-03T09:55:58Z (about 1 year ago)
Improve definition wording

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
The triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
In summary, the triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#9: Post edited by

trichoplax‭ · 2023-10-03T09:52:33Z (about 1 year ago)
Specify inputs cannot be assumed to be sorted

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Markdown

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
The triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
~~- This may be 3 separate inputs, or any ordered or unordered data structure.~~
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
The triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be as 3 separate inputs, or any ordered data structure.
- Your code must work for integers in any order (you must not assume that they are sorted).
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#8: Post edited by

trichoplax‭ · 2023-10-03T09:25:26Z (about 1 year ago)
Mention Borromean rings

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
The triple of integers is coprime, but removing any single integer leaves a pair of integers that are not coprime. The name is by analogy with [Borromean rings](https://en.m.wikipedia.org/wiki/Borromean_rings).
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#7: Post edited by

trichoplax‭ · 2023-10-03T09:08:13Z (about 1 year ago)
Specify input upper limit

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
- Your code must support input integers up to and including 127.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#6: Post edited by

trichoplax‭ · 2023-10-02T12:12:31Z (about 1 year ago)
Permute some test cases

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
12, 20, 30 : false
42, 70, 105 : false
30, 105, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
6, 15, 10 : true
10, 6, 15 : true
10, 15, 6 : true
15, 6, 10 : true
15, 10, 6 : true
12, 20, 30 : false
12, 30, 20 : false
20, 12, 30 : false
20, 30, 12 : false
30, 12, 20 : false
30, 20, 12 : false
42, 70, 105 : false
42, 105, 70 : false
70, 42, 105 : false
70, 105, 42 : false
105, 42, 70 : false
105, 70, 42 : false
14, 30, 105 : true
14, 105, 30 : true
30, 14, 105 : true
30, 105, 14 : true
105, 14, 30 : true
105, 30, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#5: Post edited by

trichoplax‭ · 2023-10-02T11:20:32Z (about 1 year ago)
Fix potentially misleading wording of third example

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
~~The greatest common divisor of the triple is 1, and the greatest common divisors of each pair are:~~
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
~~The greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.~~
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
12, 20, 30 : false
42, 70, 105 : false
30, 105, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of the triple is 1, and the greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
12, 20, 30 : false
42, 70, 105 : false
30, 105, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#4: Post edited by

trichoplax‭ · 2023-10-02T02:28:23Z (about 1 year ago)
Simplify

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
~~For the purposes of this challenge, the following definition will be used:~~
~~- 3 positive integers are called ***Borromean coprimes*** if both of the following are true:~~
~~- Their greatest common divisor is 1.~~
~~- The greatest common divisor of every pair is greater than 1.~~
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
## Output
~~- Choose 2 distinct values to represent "true" and "false".~~
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisor of the triple is 1, and the greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
All of the GCDs are greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
12, 20, 30 : false
42, 70, 105 : false
30, 105, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
## Output
- 1 of 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisor of the triple is 1, and the greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
The greatest common divisor of every pair is greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
You may use any 2 distinct values instead of "true" and "false".
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
12, 20, 30 : false
42, 70, 105 : false
30, 105, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#3: Post edited by

trichoplax‭ · 2023-10-02T00:22:21Z (about 1 year ago)
Make second example more distinct from the first

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
For the purposes of this challenge, the following definition will be used:
- 3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
## Output
- Choose 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
~~- Input: `2, 3, 4`~~
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisor of the triple is 1, and the greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
All of the GCDs are greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
12, 20, 30 : false
42, 70, 105 : false
30, 105, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
For the purposes of this challenge, the following definition will be used:
- 3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
## Output
- Choose 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 5`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisor of the triple is 1, and the greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
All of the GCDs are greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
12, 20, 30 : false
42, 70, 105 : false
30, 105, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#2: Post edited by

trichoplax‭ · 2023-10-02T00:19:40Z (about 1 year ago)
Remove superfluous input rule

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Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
For the purposes of this challenge, the following definition will be used:
- 3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
- Here "integer" means a number with zero fractional part. This does not need to be a data type named "integer". For example, you are free to take input as floating point numbers that happen to have zero fractional part.
## Output
- Choose 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 4`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisor of the triple is 1, and the greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
All of the GCDs are greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
12, 20, 30 : false
42, 70, 105 : false
30, 105, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

Given 3 positive integers, indicate whether they are Borromean coprimes.
## Definition
For the purposes of this challenge, the following definition will be used:
- 3 positive integers are called ***Borromean coprimes*** if both of the following are true:
- Their greatest common divisor is 1.
- The greatest common divisor of every pair is greater than 1.
## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
## Output
- Choose 2 distinct values to represent "true" and "false".
## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`
The greatest common divisor of the triple is 2, so these are not Borromean coprimes.
### GCD equal to 1 for a pair
- Input: `2, 3, 4`
- Output: `false`
The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.
### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`
The greatest common divisor of the triple is 1, and the greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5
All of the GCDs are greater than 1, so these are Borromean coprimes.
## Test cases
Test cases are in the format `comma, separated, inputs : output`.
```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
12, 20, 30 : false
42, 70, 105 : false
30, 105, 14 : true
```
## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.
> Explanations are optional, but I'm more likely to upvote answers that have one.
[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

#1: Initial revision by

trichoplax‭ · 2023-10-01T23:08:21Z (about 1 year ago)

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Borromean coprimes

Given 3 positive integers, indicate whether they are Borromean coprimes.

## Definition
For the purposes of this challenge, the following definition will be used:

- 3 positive integers are called ***Borromean coprimes*** if both of the following are true:
    - Their greatest common divisor is 1.
    - The greatest common divisor of every pair is greater than 1.

## Input
- 3 positive integers.
- This may be 3 separate inputs, or any ordered or unordered data structure.
- Here "integer" means a number with zero fractional part. This does not need to be a data type named "integer". For example, you are free to take input as floating point numbers that happen to have zero fractional part.

## Output
- Choose 2 distinct values to represent "true" and "false".

## Examples
### GCD not equal to 1 for the triple
- Input: `2, 4, 6`
- Output: `false`

The greatest common divisor of the triple is 2, so these are not Borromean coprimes.

### GCD equal to 1 for a pair
- Input: `2, 3, 4`
- Output: `false`

The greatest common divisor of the pair `2, 3` is 1, so these are not Borromean coprimes.

### Borromean coprimes
- Input: `6, 10, 15`
- Output: `true`

The greatest common divisor of the triple is 1, and the greatest common divisors of each pair are:
- GCD(6, 10) = 2
- GCD(6, 15) = 3
- GCD(10, 15) = 5

All of the GCDs are greater than 1, so these are Borromean coprimes.

## Test cases
Test cases are in the format `comma, separated, inputs : output`.

```text
1, 1, 1 : false
1, 1, 2 : false
1, 1, 3 : false
1, 2, 2 : false
1, 2, 3 : false
2, 2, 2 : false
2, 2, 3 : false
2, 3, 3 : false
2, 3, 4 : false
2, 3, 5 : false
2, 4, 5 : false
2, 4, 6 : false
6, 10, 15 : true
12, 20, 30 : false
42, 70, 105 : false
30, 105, 14 : true
```

## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.

> Explanations are optional, but I'm more likely to upvote answers that have one.


[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"

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