Comments on Net or not?

Parent

Net or not?

−0

Given a hexomino, indicate whether it is a net of a cube.

Input

A 6 by 6 grid containing exactly 6 filled squares.
The 6 filled squares will be in a single edge connected set (a hexomino).
The topmost row and leftmost column will never be empty (the hexomino will be as far up and left as it can go).
The grid is represented as 6 newline separated strings of 6 characters, with # for a filled square and . for an empty square.

Output

One of 2 distinct values to indicate whether the hexomino can be folded to give a cube.

The hexominoes

A hexomino is an edge connected subset of the square tiling, composed of exactly 6 squares.

Up to rotation and reflection, there are 35 edge connected hexominoes, 11 of which are nets of a cube.

The 35 hexominoes^[1]

The 11 nets of a cube^[2]

Your code must also accept inputs that are rotations and reflections of these. There are a total of 216 hexominoes including all rotations by a multiple of 90 degrees and reflections, 64 of which are cube nets. The test cases include all of these.

Test cases

Cube nets

The 64 hexominoes that can be folded into a cube.

#.....
####..
#.....
......
......
......

.#....
.#....
.#....
###...
......
......

...#..
####..
...#..
......
......
......

###...
.#....
.#....
.#....
......
......

.##...
.#....
.#....
##....
......
......

...#..
####..
#.....
......
......
......

##....
.#....
.#....
.##...
......
......

#.....
####..
...#..
......
......
......

##....
.###..
.#....
......
......
......

#.....
###...
.#....
.#....
......
......

..#...
###...
.#....
.#....
......
......

.#....
.###..
##....
......
......
......

.#....
.#....
###...
#.....
......
......

..##..
###...
..#...
......
......
......

.#....
.#....
###...
..#...
......
......

..#...
###...
..##..
......
......
......

##....
.##...
..##..
......
......
......

#.....
##....
.##...
..#...
......
......

..##..
.##...
##....
......
......
......

..#...
.##...
##....
#.....
......
......

###...
..###.
......
......
......
......

..###.
###...
......
......
......
......

#.....
#.....
##....
.#....
.#....
......

.#....
.#....
##....
#.....
#.....
......

.#....
###...
.#....
.#....
......
......

.#....
.#....
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.#....
......
......

..#...
####..
..#...
......
......
......

.#....
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.#....
......
......
......

.#....
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..##..
......
......
......

..#...
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......
......

##....
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..#...
......
......
......

.#....
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#.....
......
......

#.....
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.#....
......
......

..##..
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......
......
......

..#...
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......
......
......

.#....
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..#...
......
......

#.....
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......
......

..##..
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......
......

##....
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......
......

.##...
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#.....
......
......

##....
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...#..
......
......
......

#.....
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......
......
......

..#...
.##...
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......
......

...#..
.###..
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......
......
......

...#..
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..#...
......
......
......

.##...
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.#....
.#....
......
......

##....
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.#....
.#....
......
......

.#....
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#.....
......
......
......

#.....
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.#....
......
......
......

.#....
.#....
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......
......

.#....
.#....
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......
......

..#...
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...#..
......
......
......

.#....
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.#....
......
......

.#....
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..#...
......
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......

..#...
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......
......
......

.#....
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.#....
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.#....
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#.....
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......

..#...
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#.....
......
......
......

...#..
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.#....
......
......
......

.#....
####..
...#..
......
......
......

Not cube nets

The 152 hexominoes that cannot be folded into a cube.

..#...
#####.
......
......
......
......

#####.
..#...
......
......
......
......

.#....
.#....
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.#....
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......

#.....
#.....
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......

.##...
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......
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......

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......

.#....
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......
......

##....
.####.
......
......
......
......

####..
...##.
......
......
......
......

#.....
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.#....
.#....
......

...##.
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......
......
......
......

.#....
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#.....
......

#.....
#.....
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......

.#....
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#.....
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......

.####.
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......

.#....
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#.....
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..#...
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#.....
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..#...
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......

#.....
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......
......

.###..
.#....
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......

#.....
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......

..##..
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##....
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####..
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......

.#....
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......

..##..
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......

#.....
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......

##....
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.#....
.#....
......
......

##....
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......
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......

##....
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......

####..
..##..
......
......
......
......

####..
.#....
.#....
......
......
......

..#...
..#...
####..
......
......
......

..#...
..#...
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..#...
......
......

#.....
#.....
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#.....
......
......

#.....
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#.....
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......
......

####..
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..#...
......
......
......

.#....
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......
......

..#...
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......
......

####..
#.#...
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......

.#....
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......

#.#...
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#.....
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#.....
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......

##....
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.#....
......
......

.#.#..
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......
......
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......

####..
.#.#..
......
......
......
......

##....
#.....
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......
......

...#..
...#..
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......
......
......

####..
...#..
...#..
......
......
......

..#...
..#...
..#...
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......
......

###...
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..#...
..#...
......
......

###...
#.....
#.....
#.....
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#.....
#.....
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#.....
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......

####..
#.....
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......

.##...
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......

#.#...
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##....
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.#....
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#.#...
......
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##....
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#.....
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..#...
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.##...
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.##...
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##....
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##....
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.##...
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#.....
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..#...
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......

###...
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#.....
......
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######
......
......
......
......
......

#.....
#.....
#.....
#.....
#.....
#.....

.###..
##....
.#....
......
......
......

.#....
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#.....
#.....
......
......

.#....
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..#...
..#...
......
......

..#...
..#...
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.#....
......
......

###...
..##..
..#...
......
......
......

.#....
##....
.###..
......
......
......

..#...
..##..
###...
......
......
......

#.....
#.....
###...
.#....
......
......

#.#...
###...
#.....
......
......
......

#.#...
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..#...
......
......
......

#.....
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#.#...
......
......
......

##....
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......
......
......

..#...
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#.#...
......
......
......

###...
.#....
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......
......
......

.##...
.#....
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......
......
......

###...
.#....
.##...
......
......
......

###...
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......
......
......
......

##....
##....
##....
......
......
......

#####.
....#.
......
......
......
......

....#.
#####.
......
......
......
......

#####.
#.....
......
......
......
......

##....
#.....
#.....
#.....
#.....
......

.#....
.#....
.#....
.#....
##....
......

#.....
#.....
#.....
#.....
##....
......

##....
.#....
.#....
.#....
.#....
......

#.....
#####.
......
......
......
......

#.....
#.#...
###...
......
......
......

###...
#.....
##....
......
......
......

###...
#.#...
#.....
......
......
......

###...
..#...
.##...
......
......
......

##....
#.....
###...
......
......
......

###...
#.#...
..#...
......
......
......

..#...
#.#...
###...
......
......
......

.##...
..#...
###...
......
......
......

###...
.###..
......
......
......
......

.#....
##....
##....
#.....
......
......

#.....
##....
##....
.#....
......
......

.###..
###...
......
......
......
......

##....
.##...
..#...
..#...
......
......

###...
..##..
...#..
......
......
......

..#...
..#...
.##...
##....
......
......

.##...
##....
#.....
#.....
......
......

.###..
##....
#.....
......
......
......

#.....
##....
.###..
......
......
......

#.....
#.....
##....
.##...
......
......

...#..
..##..
###...
......
......
......

.##...
####..
......
......
......
......

#.....
##....
##....
#.....
......
......

.#....
##....
##....
.#....
......
......

####..
.##...
......
......
......
......

##....
.#....
##....
#.....
......
......

##....
#.....
##....
.#....
......
......

##.#..
.###..
......
......
......
......

.###..
##.#..
......
......
......
......

#.##..
###...
......
......
......
......

.#....
##....
#.....
##....
......
......

###...
#.##..
......
......
......
......

#.....
##....
.#....
##....
......
......

.#....
##....
.#....
.#....
.#....
......

...#..
#####.
......
......
......
......

#.....
#.....
#.....
##....
#.....
......

.#....
#####.
......
......
......
......

.#....
.#....
.#....
##....
.#....
......

#####.
...#..
......
......
......
......

#.....
##....
#.....
#.....
#.....
......

#####.
.#....
......
......
......
......

#..#..
####..
......
......
......
......

##....
.#....
.#....
##....
......
......

####..
#..#..
......
......
......
......

##....
#.....
#.....
##....
......
......

Scoring

This is a code golf challenge. Your score is the number of bytes in your code. Lowest score for each language wins.

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

Thanks to The 35 hexominoes Wikimedia page. ↩︎
Thanks to The 11 nets of a cube Wikimedia page. ↩︎

code-golf math

posted 10 months ago

CC BY-SA 4.0

trichoplax‭

1215 reputation 98 21 156 501

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is a duplicate

This question has been asked before and has already been answered. It should be marked as a duplicate.

Please enter the URL of the proposed duplicate in the details field below.

not constructive

This question cannot be answered in a way that is helpful to anyone. It's not possible to learn something from possible answers, except for the solution for the specific problem of the asker.

−0

[Python 3], 463 400 343 bytes …

3h ago

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Post

−0

Python 3, 463 400 343 bytes

-63 bytes thanks to trichoplax's suggestion to remove spaces
-57 bytes by simple conversion to base 36

where'dmyspacebarsgoinmypreviousedit?anyways,

lambda s:hex(sum(2**i*(c=='#')for i,c in enumerate(s)))[2:]in hex(int("am771a6n2yfu7ug75zes2q1su0f6gkn02oqfhz3lrnkgshfw089ql9jt5ij15gcgdkbqvvgs988w3jrz2rteixg1m9g6x9zjwwo6121ad1jae2vlb9n6exq73631tpgp0fjvemidcr1jm7vipjsxv7rsos2srbt5456mb79qqxiod0ay2tk927y060mqwiv8ggkn9565h93c2j3xrvd5jxcu4p2egw5qkh6rzcfrhsnqr2gn6i6vr5t3hj89xbgp0m51f",base=36))

Try it online!

Yet another interesting challenge foiled to brute force... (at least until someone comes up with a way to decision-problem this more efficiently...)

Anonymous lambda function which takes string as input. Takes a power of 2 from the character indexes, indicating #s with 1s and .s/newlines with 0s. Sums up and manually checks a lookup table for all valid cube nets. Returns True for cube nets and False otherwise.

(i.e. if # means include and ./\n mean exclude, 1st character has value 1, 2nd charcter has value 2, 3rd character has value 4, then values 8, 16, 32, and so on with all powers of 2 up to 2⁴⁰ inclusive)

posted 4 days ago

CC BY-SA 4.0

3h ago

hydroxyl-radical‭

36 reputation 1 2 5 14

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3 comment threads

Probable improvements (1 comment)

Omitting the spaces (3 comments)

Base 36 (4 comments)

trichoplax‭ wrote 2 days ago

copy link

The spaces in the long string of true cases can't all be removed, because that would sometimes cause the end of one number and the beginning of the next to join together and make one of the false cases present in the string, causing a test case failure.

However, this problem only affects 6 of the spaces, so the other 57 can be removed:

lambda s:hex(sum(2**i*(c=='#')for i,c in enumerate(s)))[2:]in"1020c1021038c 10703107811078210784107882040c081207032078120782207842078820c10620c30220c30421c1023030330381303823038439c40810740818640830340838140838240838440c10640c30240c30441810341818141818241c102438c4781478247844788608106608302608304618102818103 81818181818281c102838c8703 8781 878287848788c08103 c08181 c08182c0c102c30cc702c704c708e07e08102"