# Research Ideas

Does anyone have any good ideas for a research paper on group theory (particularity the Rubik's Cube, but anything within the topic works)? It's for a IB math extended essay (for high school), and it seems many people here are cubers. So far i've considered investigating solvability of random configurations, but the only real way I've found is to solve it as much as possible until you either finish or get to an un-solvable state. I've also considered investigating the Devil's Algorithm (one that can solve any cube if repeated long enough) but I don't know if the rubik's cube group can be represented as a permutation group. Any ideas are very much appreciated!

Note by Manasa Kaniselvan
5 years ago

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See here and here : it does form a permutation group, as each element of the 'state-of-the-cube' group is just an arrangement (permutation) of colours of the cube. However, some colour combinations are physically impossible if you require that it be possible to complete the cube, so it doesn't form a symmetric group [containing all permutations of the set of 'colours-in-a-space']. Given that it seems the Rubik's cube has been flogged to death and beyond by people doing projects in group theory, it may be worth looking for a lesser-known group in nature.

- 5 years ago

Yes, I've realized that after looking through some sample EEs. Now I'm thinking of doing an Olympiad problem and generalizing it.

- 5 years ago

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شركة مكافحة حشرات بالدمام والقطيف وراس التنورة وبقيق انوار يطبية لتنظيف المنازل وتنظيف الخزانات بالقطيف وتنظيف الشقق والبويت وتنظيف العمائر والفلل بالدمام والقطيف وراس التنورة وبقيق ومكافحة البق والنمل الابيض بالقطيف والدمام http://goo.gl/UzRGnv شركة مكافحة حشرات بالخبر http://cleaning-dammam.com/2015/11/01/termite-control-company-in-dammam/ شركة مكافحة النمل الابيض بالدمام http://cleaning-dammam.com/2015/12/10/washing-and-tank-cleaning-company-qatif/ شركة تنظيف خزانات بالقطيف http://cleaning-dammam.com/2015/11/29/company-combating-bed-bugs-in-dammam/ شركة مكافحة البق بالدمام http://cleaning-dammam.com/2015/11/27/pest-control-companies-qatif-2/ http://cleaning-dammam.com/2015/11/20/termite-control-company-bbakiq/ http://cleaning-dammam.com/2015/11/01/termite-control-company-qatif/ http://cleaning-dammam.com/2015/11/02/pest-control-companies-qatif/ http://cleaning-dammam.com/2015/11/02/anti-bugs-company-in-dammam/ http://cleaning-dammam.com/2015/11/05/anti-bugs-and-cockroaches-qatif-company/ http://cleaning-dammam.com/2015/11/06/company-combating-bugs-and-termites-qatif/ https://www.youtube.com/watch?v=Eh2JxBtJ4 http://cleaning-dammam.com/2015/11/12/how-to-combat-bugs-qatif/ http://cleaning-dammam.com/2015/11/06/company-combating-bugs-and-termites-in-dammam/ http://cleaning-dammam.com/2015/10/21/pest-control-company-qatif/ http://cleaning-dammam.com/2015/10/21/the-facades-of-buildings-washing-company-in-dammam/ http://cleaning-dammam.com/2015/10/21/washing-and-cleaning-company-villas-in-dammam/ http://cleaning-dammam.com/2015/10/18/washing-and-cleaning-company-amaar-dammam/ http://cleaning-dammam.com/2015/10/18/carpets-washing-qatif-company/ http://cleaning-dammam.com/2015/10/16/swimming-pools-washing-company-in-dammam/ http://cleaning-dammam.com/2015/10/16/sofas-washing-company-with-perfuming-qatif/ http://cleaning-dammam.com/2015/10/16/washing-carpet-company-in-dammam/ http://cleaning-dammam.com/2015/10/16/tatters-washing-company-in-dammam/ http://cleaning-dammam.com/2015/10/16/aldoblexat-washing-qatif-company/ http://cleaning-dammam.com/2015/10/15/company-cleaning-and-sterilizing-tanks-in-dammam/ http://cleaning-dammam.com/2015/10/15/cleaning-company-mosques-in-dammam/ http://cleaning-dammam.com/2015/10/15/cleaning-parks-in-dammam/ http://cleaning-dammam.com/2015/10/14/%d8%b4%d8%b1%d9%83%d8%a9-%d8%aa%d9%86%d8%b8%d9%8a%d9%81-%d8%ae%d8%b2%d8%a7%d9%86%d8%a7%d8%aa-%d8%a8%d8%a7%d9%84%d8%af%d9%85%d8%a7%d9%85/ http://cleaning-dammam.com/2015/10/27/%d8%b4%d8%b1%d9%83%d8%a9-%d8%aa%d9%86%d8%b8%d9%8a%d9%81-%d9%85%d8%af%d8%a7%d8%b1%d8%b3-%d8%a8%d8%a7%d9%84%d8%af%d9%85%d8%a7%d9%85/ http://cleaning-dammam.com/2015/10/24/cleaning-houses-qatif-company/ http://cleaning-dammam.com/2015/10/24/cleaning-houses-rastanorah-company/ http://cleaning-dammam.com/2015/10/24/cleaning-houses-bbakiq-company/ http://cleaning-dammam.com/2015/10/24/company-termite-control-and-black-qatif/ http://cleaning-dammam.com/2015/10/24/company-cleaning-swimming-pools-qatif/ http://cleaning-dammam.com/2015/10/22/cleaning-company-in-dammam/ http://cleaning-dammam.com/2015/10/22/%d8%b4%d8%b1%d9%83%d8%a9-%d9%86%d8%b8%d8%a7%d9%81%d8%a9-%d8%a8%d8%b1%d8%a3%d8%b3-%d8%aa%d9%86%d9%88%d8%b1%d8%a9/ http://cleaning-dammam.com/2015/10/22/general-cleanliness-bbakiq-company/ http://cleaning-dammam.com/2015/10/22/anti-bugs-company-qatif/ http://cleaning-dammam.com/category/%D8%AE%D8%AF%D9%85%D8%A7%D8%AA-%D8%A7%D9%84%D8%AA%D9%86%D8%B8%D9%8A%D9%81-%D8%A8%D8%A7%D9%84%D9%85%D9%86%D8%B7%D9%82%D8%A9-%D8%A7%D9%84%D8%B4%D8%B1%D9%82%D9%8A%D8%A9/ http://cleaning-dammam.com/category/%D8%AE%D8%AF%D9%85%D8%A7%D8%AA-%D9%85%D9%83%D8%A7%D9%81%D8%AD%D8%A9-%D8%A7%D9%84%D8%AD%D8%B4%D8%B1%D8%A7%D8%AA-%D8%A8%D8%A7%D9%84%D9%85%D9%86%D8%B7%D9%82%D8%A9-%D8%A7%D9%84%D8%B4%D8%B1%D9%82%D9%8A/

- 1 year, 11 months ago

مؤسسة صفوة المدينة شركة تنظيف خزانات وغسيل خزانات بالمدينة المنورة ومكافحة حشرات بالمدينة المنورة الشركة لديها تخصص فى نقل العفش بالمدينة اللمنورة ومكافحة الحشرات وغسيل الخزانات بالمدينة المنورة http://www.atar-almadinah.com/khasil.html شركة تنظيف خزانات بالمدينة المنورة

- 1 year, 11 months ago

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- 1 year, 11 months ago

شركه تنظيف منازل بالمدينه المنوره لديه القدرة على العمل فى جميع شتى مجالات التنظيف بالمدينة المنورة لذلك ننل ثقة عملاؤنا بكل مصداقية عاليه حتى نكسب احسن شركة تنظيف بالمدينة المنورة تنظيف شقق بالمدينة المنورة تنظيف فلل بالمدينة المنورة تنظيف خزانات بالمدينة المنورة http://tasaheelteeba.com/?p=68 شركة تنظيف منازل بالمدينة المنورة http://tasaheelteeba.com/?p=46 شركة مكافحة حشرات بالمدينة المنورة http://tasaheelteeba.com/?p=41 شركة كشف تسربات بالمدينة المنورة http://tasaheelteeba.com/?p=38 شركة تنظيف كنب بالمدينة المنورة http://tasaheelteeba.com/?p=21 شركة تنظيف وغسيل الخزانات بالمدينة المنورة http://tasaheelteeba.com/?p=8 شركة نقل العفش بالمدينة المنورة http://tasaheelteeba.com/?p=215 شركة غسيل كنب بالمدينة المنورة http://tasaheelteeba.com/?p=225 شركة عزل خزانات بالمدينة المنورة http://tasaheelteeba.com/?p=192 شراء الاثاث المستعمل بالمدينة المنورة http://tasaheelteeba.com/?p=99 شراء اثاث مستعمل بالمدينة المنورة http://tasaheelteeba.com

- 1 year, 11 months ago

فرسان النيل هى الاولى فى نقل العفش بالدمام هي شركة نقل عفش بالخبر وشركة نقل عفش بالجبيل والدمام وشركة نقل عفش بالقطيف والدمام وشركة نقل عفش بالاحساء وشركة نقل عفش بقيق وراس التنورة http://forsan-elnil.com/arabic/?id=1 شركة نقل عفش بالدمام http://forsan-elnil.com/ شركات نقل الاثاث والعفش بالدمام http://forsan-elnil.com/arabic/index.php?id=6 شركة تنظيف بالجبيل http://forsan-elnil.com/arabic/index.php?id=2 شركة نقل اثاث بالجبيل http://forsan-elnil.com/arabic/index.php?id=3 شركة نقل اثاث بالخبر http://forsan-elnil.com/arabic/index.php?id=5 شركة نقل اثاث بالقطيف

- 1 year, 11 months ago

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- 1 year, 11 months ago

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- 2 years ago

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- 2 years ago

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- 2 years ago

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- 2 years ago

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- 2 years ago

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- 2 years ago

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- 2 years, 2 months ago

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- 2 years, 10 months ago

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- 2 years, 10 months ago

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- 2 years, 11 months ago

- 2 years, 11 months ago

- 2 years, 11 months ago

- 3 years, 3 months ago

I am trying to do an EE on Rubik's Cube, too. But my goal is to find total number of legal permutations of the cube group and find a way to mathematically describe Rubik's cube. I have represented the cube as a cyclic subgroup of a larger symmetric group, but I am having difficulties to represent algorithms for solutions. Can anyone help me? Thanks in advance

- 3 years, 9 months ago

Not sure if there is a solution but with the commutators for the Rubik's cube is there a minimum # of moves that any Rubik's cube configuration could be solved in? (this might already be proven / solved)

- 5 years ago

Think about what you like most in the IB syllabus.

- 5 years ago

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