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Minimum effort to detect a solved Rubik's Cube
Why is a single-corner twist not a valid position on a Rubik's cube?What is the superflip on the 4x4x4 Rubik's cube?3x3x3 Rubik's Cube Illegal StateHow many cubes can we fit in?Where is my girlfriend?Magnetic Rubik's cubeRubik's Chess PuzzleCan a single side of a Rubik's Cube legally contain all possible combinations of colors?Unsolvable enigmatic 3x3x3 Rubik's cube?Can this Rubik's cube be solved?
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$begingroup$
When writing a program to permute a Rubik's Cube and then subsequently detect whether it is solved or not, what is the absolute minimum amount of programmatic effort required to determine if the cube is solved?
One can obviously check all six sides to determine if the cube is solved, and return early if anything appears out of order. One can also reduce that effort, by always ignoring one side, since five solved sides implies that the sixth side is solved.
Are there any other optimizations one can introduce?
Note: My attempts at googling this answer ended up with a lot of cube solving materials, and some code that actually detects solved cubes, but nothing in the way of optimal solutions to programmatically detecting a solved cube.
rubiks-cube
asked 8 hours ago
Chuck WolberChuck Wolber
1434 bronze badges
New contributor
Chuck Wolber is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
$begingroup$
When writing a program to permute a Rubik's Cube and then subsequently detect whether it is solved or not, what is the absolute minimum amount of programmatic effort required to determine if the cube is solved?
One can obviously check all six sides to determine if the cube is solved, and return early if anything appears out of order. One can also reduce that effort, by always ignoring one side, since five solved sides implies that the sixth side is solved.
Are there any other optimizations one can introduce?
Note: My attempts at googling this answer ended up with a lot of cube solving materials, and some code that actually detects solved cubes, but nothing in the way of optimal solutions to programmatically detecting a solved cube.
rubiks-cube
asked 8 hours ago
Chuck WolberChuck Wolber
1434 bronze badges
New contributor
Chuck Wolber is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
When writing a program to permute a Rubik's Cube and then subsequently detect whether it is solved or not, what is the absolute minimum amount of programmatic effort required to determine if the cube is solved?
One can obviously check all six sides to determine if the cube is solved, and return early if anything appears out of order. One can also reduce that effort, by always ignoring one side, since five solved sides implies that the sixth side is solved.
Are there any other optimizations one can introduce?
Note: My attempts at googling this answer ended up with a lot of cube solving materials, and some code that actually detects solved cubes, but nothing in the way of optimal solutions to programmatically detecting a solved cube.
rubiks-cube
asked 8 hours ago
Chuck WolberChuck Wolber
1434 bronze badges
New contributor
Chuck Wolber is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
When writing a program to permute a Rubik's Cube and then subsequently detect whether it is solved or not, what is the absolute minimum amount of programmatic effort required to determine if the cube is solved?
One can obviously check all six sides to determine if the cube is solved, and return early if anything appears out of order. One can also reduce that effort, by always ignoring one side, since five solved sides implies that the sixth side is solved.
Are there any other optimizations one can introduce?
Note: My attempts at googling this answer ended up with a lot of cube solving materials, and some code that actually detects solved cubes, but nothing in the way of optimal solutions to programmatically detecting a solved cube.
rubiks-cube
rubiks-cube
asked 8 hours ago
Chuck WolberChuck Wolber
1434 bronze badges
New contributor
Chuck Wolber is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
Chuck WolberChuck Wolber
1434 bronze badges
New contributor
Chuck Wolber is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
Chuck WolberChuck Wolber
1434 bronze badges
New contributor
Chuck Wolber is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 8 hours ago
Chuck WolberChuck Wolber
1434 bronze badges
asked 8 hours ago
Chuck WolberChuck Wolber
1434 bronze badges
1434 bronze badges
New contributor
Chuck Wolber is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Chuck Wolber is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I think:
2 solved opposite layers and 3 of the remaining edges (from 4) is optimal
Also
3 faces in a horseshoe and a missing edge (from 2)
This leaves:
3 orthogonal faces and 2 of the missing edges (from 3)
Beyond this:
Any combination of 4 faces involves one of the above cases.
answered 8 hours ago
JonMark PerryJonMark Perry
24.7k6 gold badges46 silver badges107 bronze badges
$endgroup$
2
$begingroup$
Maybe I'm misunderstanding something, but about the first one, don't you mean layers (so the complete 2/3 -sided cubies) instead of faces (a side of 3x3 stickers)? If not, how would you differentiate from a solved cube and let's say this cube? The white/yellow faces are solved, as well as the four edges in the middle layer.
$endgroup$
– Kevin Cruijssen
7 hours ago
1
$begingroup$
@KevinCruijssen; good point, I've fixed it.
$endgroup$
– JonMark Perry
7 hours ago
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I think:
2 solved opposite layers and 3 of the remaining edges (from 4) is optimal
Also
3 faces in a horseshoe and a missing edge (from 2)
This leaves:
3 orthogonal faces and 2 of the missing edges (from 3)
Beyond this:
Any combination of 4 faces involves one of the above cases.
answered 8 hours ago
JonMark PerryJonMark Perry
24.7k6 gold badges46 silver badges107 bronze badges
$endgroup$
2
$begingroup$
Maybe I'm misunderstanding something, but about the first one, don't you mean layers (so the complete 2/3 -sided cubies) instead of faces (a side of 3x3 stickers)? If not, how would you differentiate from a solved cube and let's say this cube? The white/yellow faces are solved, as well as the four edges in the middle layer.
$endgroup$
– Kevin Cruijssen
7 hours ago
1
$begingroup$
@KevinCruijssen; good point, I've fixed it.
$endgroup$
– JonMark Perry
7 hours ago
add a comment |
$begingroup$
I think:
2 solved opposite layers and 3 of the remaining edges (from 4) is optimal
Also
3 faces in a horseshoe and a missing edge (from 2)
This leaves:
3 orthogonal faces and 2 of the missing edges (from 3)
Beyond this:
Any combination of 4 faces involves one of the above cases.
answered 8 hours ago
JonMark PerryJonMark Perry
24.7k6 gold badges46 silver badges107 bronze badges
$endgroup$
2
$begingroup$
Maybe I'm misunderstanding something, but about the first one, don't you mean layers (so the complete 2/3 -sided cubies) instead of faces (a side of 3x3 stickers)? If not, how would you differentiate from a solved cube and let's say this cube? The white/yellow faces are solved, as well as the four edges in the middle layer.
$endgroup$
– Kevin Cruijssen
7 hours ago
1
$begingroup$
@KevinCruijssen; good point, I've fixed it.
$endgroup$
– JonMark Perry
7 hours ago
add a comment |
$begingroup$
I think:
2 solved opposite layers and 3 of the remaining edges (from 4) is optimal
Also
3 faces in a horseshoe and a missing edge (from 2)
This leaves:
3 orthogonal faces and 2 of the missing edges (from 3)
Beyond this:
Any combination of 4 faces involves one of the above cases.
answered 8 hours ago
JonMark PerryJonMark Perry
24.7k6 gold badges46 silver badges107 bronze badges
$endgroup$
I think:
2 solved opposite layers and 3 of the remaining edges (from 4) is optimal
Also
3 faces in a horseshoe and a missing edge (from 2)
This leaves:
3 orthogonal faces and 2 of the missing edges (from 3)
Beyond this:
Any combination of 4 faces involves one of the above cases.
answered 8 hours ago
JonMark PerryJonMark Perry
24.7k6 gold badges46 silver badges107 bronze badges
edited 7 hours ago
answered 8 hours ago
JonMark PerryJonMark Perry
24.7k6 gold badges46 silver badges107 bronze badges
answered 8 hours ago
JonMark PerryJonMark Perry
24.7k6 gold badges46 silver badges107 bronze badges
answered 8 hours ago
JonMark PerryJonMark Perry
24.7k6 gold badges46 silver badges107 bronze badges
24.7k6 gold badges46 silver badges107 bronze badges
2
$begingroup$
Maybe I'm misunderstanding something, but about the first one, don't you mean layers (so the complete 2/3 -sided cubies) instead of faces (a side of 3x3 stickers)? If not, how would you differentiate from a solved cube and let's say this cube? The white/yellow faces are solved, as well as the four edges in the middle layer.
$endgroup$
– Kevin Cruijssen
7 hours ago
1
$begingroup$
@KevinCruijssen; good point, I've fixed it.
$endgroup$
– JonMark Perry
7 hours ago
add a comment |
2
$begingroup$
Maybe I'm misunderstanding something, but about the first one, don't you mean layers (so the complete 2/3 -sided cubies) instead of faces (a side of 3x3 stickers)? If not, how would you differentiate from a solved cube and let's say this cube? The white/yellow faces are solved, as well as the four edges in the middle layer.
$endgroup$
– Kevin Cruijssen
7 hours ago
1
$begingroup$
@KevinCruijssen; good point, I've fixed it.
$endgroup$
– JonMark Perry
7 hours ago
2
2
$begingroup$
Maybe I'm misunderstanding something, but about the first one, don't you mean layers (so the complete 2/3 -sided cubies) instead of faces (a side of 3x3 stickers)? If not, how would you differentiate from a solved cube and let's say this cube? The white/yellow faces are solved, as well as the four edges in the middle layer.
$endgroup$
– Kevin Cruijssen
7 hours ago
$begingroup$
Maybe I'm misunderstanding something, but about the first one, don't you mean layers (so the complete 2/3 -sided cubies) instead of faces (a side of 3x3 stickers)? If not, how would you differentiate from a solved cube and let's say this cube? The white/yellow faces are solved, as well as the four edges in the middle layer.
$endgroup$
– Kevin Cruijssen
7 hours ago
1
1
$begingroup$
@KevinCruijssen; good point, I've fixed it.
$endgroup$
– JonMark Perry
7 hours ago
$begingroup$
@KevinCruijssen; good point, I've fixed it.
$endgroup$
– JonMark Perry
7 hours ago
add a comment |
Chuck Wolber is a new contributor. Be nice, and check out our Code of Conduct.
Chuck Wolber is a new contributor. Be nice, and check out our Code of Conduct.
Chuck Wolber is a new contributor. Be nice, and check out our Code of Conduct.
Chuck Wolber is a new contributor. Be nice, and check out our Code of Conduct.
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