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An $n$-polyomino is a connected subset of the square tiling consisting of $n$ squares. We will not require that polyominos be simply connected, that is they can have holes. We will say a $n$-polyo...
#4: Post edited
by
WheatWizard
·
2023-06-17T23:42:22Z (11 months ago)
More examples.
- An $n$-polyomino is a connected subset of the square tiling consisting of $n$ squares. We will not require that polyominos be simply connected, that is they can have holes.
- We will say a $n$-polyomino is *prime* if it cannot be disected into disjoint $k$-polyominos for any 1<$k$<$n$. For example this square 4-polyomino:
- ```text
- XX
- XX
- ```
- can be dissected into two 2-polyominos, but this "T"-shaped 4-polyomino cannot:
- ```text
- XXX
- X
- ```
- The $k$-polyominos do not need to be equal for example:
- ```text
- XXXXX
- X XX
- ```
- This 8-polyomino can be subdivided into the two polyominos shown in the last examples. They are not equal but they are both 4-polyominos so the example is not prime.
- Naturally if $n$ is a prime number all $n$-polyominos are prime, however as shown above there are prime $n$-polyominos where $n$ is not prime. Here are examples for the next couple composite numbers
- ### 6
- ```text
- X
- XXXX
- X
- ```
- ### 8
- ```text
- X
- XXXXX
- X X
- ```
- ### 9
- ```text
- XXXXXXXX
- X
- ```
- ## Challenge
- Given a polyomino as input output one consistent value if it is prime and another consistent distinct value if it is not prime.
- This is code-golf the goal being to minimize the size of your source code as measured in bytes.
- An $n$-polyomino is a connected subset of the square tiling consisting of $n$ squares. We will not require that polyominos be simply connected, that is they can have holes.
- We will say a $n$-polyomino is *prime* if it cannot be disected into disjoint $k$-polyominos for any 1<$k$<$n$. For example this square 4-polyomino:
- ```text
- XX
- XX
- ```
- can be dissected into two 2-polyominos, but this "T"-shaped 4-polyomino cannot:
- ```text
- XXX
- X
- ```
- The $k$-polyominos do not need to be equal for example:
- ```text
- XXXXX
- X XX
- ```
- This 8-polyomino can be subdivided into the two polyominos shown in the last examples. They are not equal but they are both 4-polyominos so the example is not prime.
- Naturally if $n$ is a prime number all $n$-polyominos are prime, however as shown above there are prime $n$-polyominos where $n$ is not prime. Here are examples for the next couple composite numbers
- ### 6
- ```text
- X
- XXXX
- X
- ```
- ### 8
- ```text
- X
- XXXXX
- X X
- ```
- ### 9
- ```text
- XXXXXXXX
- X
- ```
- ### 10
- ```
- XXXXXX
- X
- XXX
- ```
- ### 12
- ```
- XXXXXXXXX
- X X
- X
- ```
- ### 14
- ```
- XXXXXXXXXXXX
- X X
- ```
- ### 15
- ```
- XXX
- X X X
- XXXXXX
- X X
- X
- ```
- ## Challenge
- Given a polyomino as input output one consistent value if it is prime and another consistent distinct value if it is not prime.
- This is code-golf the goal being to minimize the size of your source code as measured in bytes.
#3: Post edited
by
WheatWizard
·
2023-06-17T18:29:40Z (11 months ago)
Holes.
An $n$-polyomino is a connected subset of the square tiling consisting of $n$ squares.- We will say a $n$-polyomino is *prime* if it cannot be disected into disjoint $k$-polyominos for any 1<$k$<$n$. For example this square 4-polyomino:
- ```text
- XX
- XX
- ```
- can be dissected into two 2-polyominos, but this "T"-shaped 4-polyomino cannot:
- ```text
- XXX
- X
- ```
- The $k$-polyominos do not need to be equal for example:
- ```text
- XXXXX
- X XX
- ```
- This 8-polyomino can be subdivided into the two polyominos shown in the last examples. They are not equal but they are both 4-polyominos so the example is not prime.
- Naturally if $n$ is a prime number all $n$-polyominos are prime, however as shown above there are prime $n$-polyominos where $n$ is not prime. Here are examples for the next couple composite numbers
- ### 6
- ```text
- X
- XXXX
- X
- ```
- ### 8
- ```text
- X
- XXXXX
- X X
- ```
- ### 9
- ```text
- XXXXXXXX
- X
- ```
- ## Challenge
- Given a polyomino as input output one consistent value if it is prime and another consistent distinct value if it is not prime.
- This is code-golf the goal being to minimize the size of your source code as measured in bytes.
- An $n$-polyomino is a connected subset of the square tiling consisting of $n$ squares. We will not require that polyominos be simply connected, that is they can have holes.
- We will say a $n$-polyomino is *prime* if it cannot be disected into disjoint $k$-polyominos for any 1<$k$<$n$. For example this square 4-polyomino:
- ```text
- XX
- XX
- ```
- can be dissected into two 2-polyominos, but this "T"-shaped 4-polyomino cannot:
- ```text
- XXX
- X
- ```
- The $k$-polyominos do not need to be equal for example:
- ```text
- XXXXX
- X XX
- ```
- This 8-polyomino can be subdivided into the two polyominos shown in the last examples. They are not equal but they are both 4-polyominos so the example is not prime.
- Naturally if $n$ is a prime number all $n$-polyominos are prime, however as shown above there are prime $n$-polyominos where $n$ is not prime. Here are examples for the next couple composite numbers
- ### 6
- ```text
- X
- XXXX
- X
- ```
- ### 8
- ```text
- X
- XXXXX
- X X
- ```
- ### 9
- ```text
- XXXXXXXX
- X
- ```
- ## Challenge
- Given a polyomino as input output one consistent value if it is prime and another consistent distinct value if it is not prime.
- This is code-golf the goal being to minimize the size of your source code as measured in bytes.
#2: Post edited
by
WheatWizard
·
2023-06-14T12:44:28Z (11 months ago)
- An $n$-polyomino is a connected subset of the square tiling consisting of $n$ squares.
- We will say a $n$-polyomino is *prime* if it cannot be disected into disjoint $k$-polyominos for any 1<$k$<$n$. For example this square 4-polyomino:
- ```text
- XX
- XX
- ```
- can be dissected into two 2-polyominos, but this "T"-shaped 4-polyomino cannot:
- ```text
- XXX
- X
- ```
- Naturally if $n$ is a prime number all $n$-polyominos are prime, however as shown above there are prime $n$-polyominos where $n$ is not prime. Here are examples for the next couple composite numbers
- ### 6
- ```text
- X
- XXXX
- X
- ```
- ### 8
- ```text
- X
- XXXXX
- X X
- ```
- ### 9
- ```text
- XXXXXXXX
- X
- ```
- ## Challenge
- Given a polyomino as input output one consistent value if it is prime and another consistent distinct value if it is not prime.
- This is code-golf the goal being to minimize the size of your source code as measured in bytes.
- An $n$-polyomino is a connected subset of the square tiling consisting of $n$ squares.
- We will say a $n$-polyomino is *prime* if it cannot be disected into disjoint $k$-polyominos for any 1<$k$<$n$. For example this square 4-polyomino:
- ```text
- XX
- XX
- ```
- can be dissected into two 2-polyominos, but this "T"-shaped 4-polyomino cannot:
- ```text
- XXX
- X
- ```
- The $k$-polyominos do not need to be equal for example:
- ```text
- XXXXX
- X XX
- ```
- This 8-polyomino can be subdivided into the two polyominos shown in the last examples. They are not equal but they are both 4-polyominos so the example is not prime.
- Naturally if $n$ is a prime number all $n$-polyominos are prime, however as shown above there are prime $n$-polyominos where $n$ is not prime. Here are examples for the next couple composite numbers
- ### 6
- ```text
- X
- XXXX
- X
- ```
- ### 8
- ```text
- X
- XXXXX
- X X
- ```
- ### 9
- ```text
- XXXXXXXX
- X
- ```
- ## Challenge
- Given a polyomino as input output one consistent value if it is prime and another consistent distinct value if it is not prime.
- This is code-golf the goal being to minimize the size of your source code as measured in bytes.
#1: Initial revision
by
WheatWizard
·
2023-06-13T17:03:58Z (11 months ago)
Determine if a polyomino is "prime"
An $n$-polyomino is a connected subset of the square tiling consisting of $n$ squares. We will say a $n$-polyomino is *prime* if it cannot be disected into disjoint $k$-polyominos for any 1<$k$<$n$. For example this square 4-polyomino: ```text XX XX ``` can be dissected into two 2-polyominos, but this "T"-shaped 4-polyomino cannot: ```text XXX X ``` Naturally if $n$ is a prime number all $n$-polyominos are prime, however as shown above there are prime $n$-polyominos where $n$ is not prime. Here are examples for the next couple composite numbers ### 6 ```text X XXXX X ``` ### 8 ```text X XXXXX X X ``` ### 9 ```text XXXXXXXX X ``` ## Challenge Given a polyomino as input output one consistent value if it is prime and another consistent distinct value if it is not prime. This is code-golf the goal being to minimize the size of your source code as measured in bytes.