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Hi everyone! I've been wanting to make a thread like this for a while now. There are a lot of neat cube theory results that are accessible to those who are interested in the cube, and who have a high school or advanced middle school math background. I've compiled a list of results that I find to be useful as well as ones that I think are very interesting. The level of questions here are for those who are just starting out with the cube who would like to learn more about the theory behind twisty puzzles. If you know how to solve the cube or are beginning to learn how to speedsolve, and you find yourself interested in the

The quiz consists of a series of questions loosely related to each other. The questions will vary in difficulty, as well as in effort level to answer the question.

When answering a question, please do so within spoiler tags. [noparse]
Spoiler
[/noparse]

If you are stuck on a question, ask! Post a reply in this thread and talk it out with others who are also following this thread. We do enough competing on this forum in the forum competition area, so there will be no points awarded for the quiz. You may, however, receive Kudos from the theory experts on the forum for clever or well thought out answers to questions.

If people enjoy this thread, then I will come up with new questions.

a) one 90 degrees clockwise, the other 90 degrees counter-clockwise

b) both 180 degrees

c) both 90 degrees clockwise

d) Come up with an algorithm to rotate exactly one center on a 3x3x3 supercube by 180 degrees.

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If there is enough interest in this thread, then I will post my answers to each of these questions by Thanksgiving weekend.

Happy cubing!

*why*questions related to the cube, then you may enjoy this thread!**How the quiz works**The quiz consists of a series of questions loosely related to each other. The questions will vary in difficulty, as well as in effort level to answer the question.

**Answer the questions you find to be interesting!**When answering a question, please do so within spoiler tags. [noparse]

Your answers

If you are stuck on a question, ask! Post a reply in this thread and talk it out with others who are also following this thread. We do enough competing on this forum in the forum competition area, so there will be no points awarded for the quiz. You may, however, receive Kudos from the theory experts on the forum for clever or well thought out answers to questions.

**In short:**

Post your answers to these questions in spoiler tags. Ask questions without using spoiler tags. Answer others' questions without using spoiler tags.Post your answers to these questions in spoiler tags. Ask questions without using spoiler tags. Answer others' questions without using spoiler tags.

If people enjoy this thread, then I will come up with new questions.

**Cube Theory Quiz #1:****Question #1)**Read Ryan Heise's page on cube laws for the 3x3x3. Now, write out the cube laws for the 2x2x2.**Question #2)**Calculate the number of legal positions to a 2x2x2. Give a brief explanation for each term in your calculation. Simply providing a numerical answer to this question does not sufficiently answer the question.**Question #3)**Calculate the number of legal positions to a 3x3x3. Give a brief explanation for each term in your calculation. Simply providing a numerical answer to this question does not sufficiently answer the question.**Question #4)**Write out the "Cube Laws" for the pyraminx. The "Cube Laws" are a list of any restrictions the puzzle must satisfy to be in a "legal" state.**Question #5)**Calculate the number of legal positions to a pyraminx. Include the rotations of the outer tips in your calculation. As usual, give a brief explanation for each term in your calculation. Simply providing a numerical answer to this question does not sufficiently answer the question.**Question #6)**When solving the 4x4x4 using the standard reduction method (i.e. solve center groups, then pair up edge groups, then solve the puzzle as a 3x3x3), what is the cause of OLL parity? (Hint: It does not just "happen", you created it. Tell me how.)**Question #7)**Explain why the speedsolving A-perm alg**R' F R' B2 R F' R' B2 R2**works. You can answer this question in two ways. Either A) Explain how this algorithm changes the positions of the affected corners, then as a separate part explain how it preserves their orientation, or B) explain the structure of this algorithm and classify it for what type of algorithm it is.**Question #8)**Come up with a 5 generator algorithm on 3x3x3 that is different from my signature and explain how it works. A 5-generator is defined as an algorithm that will use 5 sides of the cube to simulate a turn of the 6th side. Try the algorithm in my signature on a solved cube to get an idea of what this looks like.**Question #9)**Come up with an algorithm to rotate two centers on a 3x3x3 supercube (if you don't have a supercube, make one!):a) one 90 degrees clockwise, the other 90 degrees counter-clockwise

b) both 180 degrees

c) both 90 degrees clockwise

d) Come up with an algorithm to rotate exactly one center on a 3x3x3 supercube by 180 degrees.

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If there is enough interest in this thread, then I will post my answers to each of these questions by Thanksgiving weekend.

Happy cubing!

Last edited: Oct 17, 2013

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Christopher Mowla