"How about sending me a fourth gimbal for Christmas?" - Michael "Mike" Collins after the Lunar Module had landed.
Applying multiple rotations is equivalent to applying a single rotation whose quaternion is equal to the product of the quaternions of the corresponding rotations.
The Rubik's Cube is a permutation by rotations, not a coloring. The question is how we can represent any resulting scramble, either as all the color fields of the cube or as specific coordinates of all the cube's elements.
Let's remember what we know:
- Rotating the cube from the initial position, we can get a total of 24 positions, and to write/solve the cube, it is enough to fix one initial position.
- Each of the 8 corners of the cube has one of 3 possible directions relative to the chosen centers, designated by the symbol § (let's call them tracs), which in total is equal to 8*3=24
- Each of the edges of the cube has one of 2 trajectories, which is also equal to 12 * 2 = 24
Now let's imagine a hedgehog with 48 needles, curled up in a ball in the center of our cube, each of whose needles is directed towards the corner or edge of the cube.
Let's designate these needles (it is possible in pairs for corners and edges) with 24 small letters of the English alphabet.
Voilà ! Now we can remove the first and last characters of our signature (it's obvious why) and write any position with 18 characters instead of 54.
P.S. If you need to track the rotation of the central (color) stickers, you can add 6 more symbols to the signature and there will be... - that's right, 24!
P.P.S. By right of the first night, let's call our (signature) encoding Catch-24.
Conclusion: Catch-24 encoding is as native as encoding color stickers of cube is easily automated, and results in a threefold reduction in recording time.
Interesting fact: 1st patent for Crown Cork with 24 teeth.
In the 1930s, testing was carried out to determine the optimal number of teeth, as the 24 teeth, that was standard, made the cap too tight and difficult to open. The current version has 21 teeth and is international standard.
Applying multiple rotations is equivalent to applying a single rotation whose quaternion is equal to the product of the quaternions of the corresponding rotations.
The Rubik's Cube is a permutation by rotations, not a coloring. The question is how we can represent any resulting scramble, either as all the color fields of the cube or as specific coordinates of all the cube's elements.
Let's remember what we know:
- Rotating the cube from the initial position, we can get a total of 24 positions, and to write/solve the cube, it is enough to fix one initial position.
- Each of the 8 corners of the cube has one of 3 possible directions relative to the chosen centers, designated by the symbol § (let's call them tracs), which in total is equal to 8*3=24
- Each of the edges of the cube has one of 2 trajectories, which is also equal to 12 * 2 = 24
Now let's imagine a hedgehog with 48 needles, curled up in a ball in the center of our cube, each of whose needles is directed towards the corner or edge of the cube.
Let's designate these needles (it is possible in pairs for corners and edges) with 24 small letters of the English alphabet.
Voilà ! Now we can remove the first and last characters of our signature (it's obvious why) and write any position with 18 characters instead of 54.
P.S. If you need to track the rotation of the central (color) stickers, you can add 6 more symbols to the signature and there will be... - that's right, 24!
P.P.S. By right of the first night, let's call our (signature) encoding Catch-24.
Conclusion: Catch-24 encoding is as native as encoding color stickers of cube is easily automated, and results in a threefold reduction in recording time.
Interesting fact: 1st patent for Crown Cork with 24 teeth.
In the 1930s, testing was carried out to determine the optimal number of teeth, as the 24 teeth, that was standard, made the cap too tight and difficult to open. The current version has 21 teeth and is international standard.
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