Waste less time on Facebook — follow Brilliant.
×

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
4 years ago

No vote yet
4 votes

Comments

Sort by:

Top Newest

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. A L · 4 years ago

Log in to reply

@A L Yes, I've realized that after looking through some sample EEs. Now I'm thinking of doing an Olympiad problem and generalizing it. Manasa Kaniselvan · 4 years ago

Log in to reply

https://khairyayman74.wordpress.com/ https://khairyayman74.wordpress.com/2015/07/14/%D8%B4%D8%B1%D9%83%D8%A9-%D8%BA%D8%B3%D9%8A%D9%84-%D8%A7%D9%84%D9%81%D9%84%D9%84-%D9%88%D8%A7%D9%84%D9%82%D8%B5%D9%88%D8%B1-%D8%A8%D8%A7%D9%84%D8%AF%D9%85%D8%A7%D9%85/ https://khairyayman74.wordpress.com/2015/07/13/%D8%A7%D9%81%D8%B6%D9%84-%D8%B4%D8%B1%D9%83%D8%A9-%D9%85%D9%83%D8%A7%D9%81%D8%AD%D8%A9-%D8%A7%D9%84%D8%B5%D8%B1%D8%A7%D8%B5%D9%8A%D8%B1-%D8%A8%D8%A7%D9%84%D8%AF%D9%85%D8%A7%D9%85/ https://khairyayman74.wordpress.com/2015/06/30/%D8%B4%D8%B1%D9%83%D8%A9-%D8%BA%D8%B3%D9%8A%D9%84-%D9%83%D9%86%D8%A8-%D8%A8%D8%A7%D9%84%D8%AF%D9%85%D8%A7%D9%85-0548923301/ https://khairyayman74.wordpress.com/2015/05/30/%D8%B4%D8%B1%D9%83%D8%A9-%D9%86%D9%82%D9%84-%D8%A7%D8%AB%D8%A7%D8%AB-%D8%A8%D8%A7%D9%84%D8%AF%D9%85%D8%A7%D9%85/ https://khairyayman74.wordpress.com/2015/06/14/%D8%BA%D8%B3%D9%8A%D9%84-%D8%A8%D8%B7%D8%B1%D9%85%D9%87-%D8%A8%D8%A7%D9%84%D8%AF%D9%85%D8%A7%D9%85-0548923301/ https://khairyayman74.wordpress.com/2015/07/23/%D8%B4%D8%B1%D9%83%D8%A9-%D9%86%D9%82%D9%84-%D8%A7%D8%AB%D8%A7%D8%AB-%D9%81%D9%89-%D8%A7%D9%84%D8%AE%D8%A8%D8%B1-0559328721/ http://www.khdmat-sa.com/2015/07/26/%D8%B4%D8%B1%D9%83%D8%A9-%D9%86%D8%B8%D8%A7%D9%81%D9%87-%D8%B9%D8%A7%D9%85%D9%87-%D8%A8%D8%A7%D9%84%D9%85%D9%86%D8%B7%D9%82%D9%87-%D8%A7%D9%84%D8%B4%D8%B1%D9%82%D9%8A%D9%87/ http://www.khdmat-sa.com/2015/07/27/%D8%B4%D8%B1%D9%83%D8%A9-%D9%86%D9%82%D9%84-%D8%A7%D9%84%D8%A7%D8%AB%D8%A7%D8%AB-%D9%81%D9%8A-%D8%A7%D9%84%D8%A7%D8%AD%D8%B3%D8%A7%D8%A1/ http://www.khdmat-sa.com/2015/07/28/%D8%B4%D8%B1%D9%83%D8%A9-%D9%86%D9%82%D9%84-%D8%A7%D9%84%D8%A7%D8%AB%D8%A7%D8%AB-%D9%81%D9%8A-%D8%A7%D9%84%D9%82%D8%B7%D9%8A%D9%81-0559328721/ https://khairyayman74.wordpress.com/2015/07/29/%D8%B4%D8%B1%D9%83%D8%A9-%D9%86%D9%82%D9%84-%D8%A7%D9%84%D8%A7%D8%AB%D8%A7%D8%AB-%D8%AF%D8%A7%D8%AE%D9%84-%D8%A7%D9%84%D8%AC%D8%A8%D9%8A%D9%84/ https://khairyayman74.wordpress.com/2015/08/05/%D8%B4%D8%B1%D9%83%D8%A9-%D8%BA%D8%B3%D9%8A%D9%84-%D9%88%D8%AA%D9%86%D8%B8%D9%8A%D9%81-%D8%AE%D8%B2%D8%A7%D9%86%D8%A7%D8%AA-%D9%81%D9%89-%D8%A7%D9%84%D9%85%D8%AF%D9%8A%D9%86%D9%87-%D8%A7%D9%84%D9%85/ https://khairyayman74.wordpress.com/2015/08/19/%D8%B4%D8%B1%D9%83%D8%A9-%D8%AA%D9%86%D8%B8%D9%8A%D9%81-%D9%85%D9%86%D8%A7%D8%B2%D9%84-%D9%81%D9%8A-%D8%A7%D9%84%D8%AF%D9%85%D8%A7%D9%85-0548923301/ https://www.youtube.com/watch?v=46UIiLjJU4U https://khairyayman74.wordpress.com/2015/08/31/%D8%B4%D8%B1%D9%83%D8%A9-%D8%BA%D8%B3%D9%8A%D9%84-%D8%A7%D9%84%D8%AE%D8%B2%D8%A7%D9%86%D8%A7%D8%AA-%D8%A8%D8%B1%D8%A7%D8%B3-%D8%A7%D9%84%D8%AA%D9%86%D9%88%D8%B1%D9%87-0556808022/ https://khairyayman74.wordpress.com/2015/09/17/%D8%B4%D8%B1%D9%83%D8%A9-%D8%AA%D9%85%D8%AF%D9%8A%D8%AF%D8%A7%D8%AA-%D8%A7%D9%84%D8%BA%D8%A7%D8%B2-%D8%A7%D9%84%D9%85%D8%B1%D9%83%D8%B2%D9%8A/ https://khairyayman74.wordpress.com/2015/09/21/%D9%85%D8%A4%D8%B3%D8%B3%D8%A9-%D8%A7%D9%84%D8%AA%D9%85%D8%AF%D9%8A%D8%AF%D8%A7%D8%AA-%D8%A7%D9%84%D8%AD%D8%AF%D9%8A%D8%AB%D9%87-0500938931/ https://khairyayman74.wordpress.com/2015/10/09/%D8%B4%D8%B1%D9%83%D8%A9-%D9%86%D9%82%D9%84-%D8%B9%D9%81%D8%B4-%D8%A8%D8%A7%D9%84%D8%A7%D8%AD%D8%B3%D8%A7%D8%A1/ https://khairyayman74.wordpress.com/2015/10/18/%D8%B4%D8%B1%D9%83%D8%A9-%D9%86%D9%82%D9%84-%D8%B9%D9%81%D8%B4-%D8%A8%D8%A7%D9%84%D8%B7%D8%A7%D8%A6%D9%81/ https://khairyayman74.wordpress.com/2016/02/23/%d8%b4%d8%b1%d9%83%d8%a9-%d9%83%d8%b4%d9%81-%d8%aa%d8%b3%d8%b1%d8%a8%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d9%8a%d8%a7%d9%87-%d8%a8%d8%a7%d9%84%d8%af%d9%85%d8%a7%d9%85/ http://eslamiatview.blogspot.com.eg/ http://eslamiatview.blogspot.com.eg/2015/09/0504194709.html http://eslamiatview.blogspot.com.eg/2015/07/blog-post.html http://eslamiatview.blogspot.com.eg/2015/09/0504194709.html http://eslamiatview.blogspot.com.eg/2015/08/blog-post.html http://eslamiatview.blogspot.com.eg/2016/04/blog-post9.html شركة نقل عفش بجدة http://eslamiatview.blogspot.com.eg/2016/04/blog-post.html شركة نقل عفش بينبع http://emcmee.blogspot.com.eg/ http://emcmee.blogspot.com.eg/2016/04/blog-post.htmlشركة نقل عفش بجدة http://emcmee.blogspot.com.eg/2016/04/blog-post11.htmlشركة نقل عفش بالطائف https://khairyayman74.wordpress.com/2016/04/11/%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%AC%D8%AF%D8%A9/ شركة تنظيف خزانات بجدة https://khairyayman74.wordpress.com/2016/04/23/%d9%85%d8%a7%d9%87%d9%89-%d8%a7%d9%84%d9%85%d9%85%d9%8a%d8%b2%d8%a7%d8%aa-%d9%84%d8%af%d9%89-%d8%b4%d8%b1%d9%83%d8%a9-%d9%86%d9%82%d9%84-%d8%b9%d9%81%d8%b4-%d8%a8%d9%85%d9%83%d8%a9%d8%9f/ https://khairyayman74.wordpress.com/2016/04/06/0537772829%d9%85%d8%a7%d9%87%d9%89-%d8%a7%d9%81%d8%b6%d9%84-%d8%b4%d8%b1%d9%83%d8%a9-%d9%86%d9%82%d9%84-%d8%b9%d9%81%d8%b4-%d8%a8%d8%a7%d9%84%d8%af%d9%85%d8%a7%d9%85%d8%9f/ https://khairyayman74.wordpress.com/2016/02/25/%d8%b4%d8%b1%d9%83%d8%a9-%d9%86%d9%82%d9%84-%d8%b9%d9%81%d8%b4-%d8%a8%d8%ac%d8%af%d8%a9/ https://khairyayman74.wordpress.com/2016/02/23/%d8%b4%d8%b1%d9%83%d8%a9-%d9%83%d8%b4%d9%81-%d8%aa%d8%b3%d8%b1%d8%a8%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d9%8a%d8%a7%d9%87-%d8%a8%d8%a7%d9%84%d8%af%d9%85%d8%a7%d9%85/ https://khairyayman74.wordpress.com/2016/02/23/%d8%b4%d8%b1%d9%83%d8%a9-%d9%86%d9%82%d9%84-%d8%a7%d9%84%d8%a7%d8%ab%d8%a7%d8%ab-%d8%a8%d8%a7%d9%84%d8%af%d9%85%d8%a7%d9%85-0564385131/ https://khairyayman74.wordpress.com/2015/11/14/%d8%b4%d8%b1%d9%83%d8%a7%d8%aa-%d9%86%d9%82%d9%84-%d8%a7%d8%ab%d8%a7%d8%ab-%d8%a8%d8%a7%d9%84%d8%ac%d8%a8%d9%8a%d9%84-0559328721/ Samar Ali · 10 months, 4 weeks ago

Log in to reply

اهم شركات كشف تسربات المياه بالدمام كذلك معرض اهم شركة مكافحة حشرات بالدمام والخبر والجبيل والخبر والاحساء والقطيف كذكل شركة تنظيف خزانات بجدة وتنظيف بجدة ومكافحة الحشرات بالخبر وكشف تسربات المياه بالجبيل والقطيف والخبر والدمام http://emc-mee.com/tanks-cleaning-company-jeddah.html شركة تنظيف خزانات بجدة http://emc-mee.com/water-leaks-detection-isolate-company-dammam.html شركة كشف تسربات المياه بالدمام http://emc-mee.com/anti-insects-company-dammam.html شركة مكافحة حشرات بالدمام

اهم شركات نقل العفش والاثاث بالدمام والخبر والجبيل اولقطيف والاحساء والرياض وجدة ومكة المدينة المنورة والخرج والطائف وخميس مشيط وبجدة افضل شركة نقل عفش بجدة نعرضها مجموعة الفا لنقل العفش بمكة والخرج والقصيم والطائف وتبوك وخميس مشيط ونجران وجيزان وبريدة والمدينة المنورة وينبع افضل شركات نقل الاثاث بالجبيل والطائف وخميس مشيط وبريدة وعنيزو وابها ونجران المدينة وينبع تبوك والقصيم الخرج حفر الباطن والظهران http://emc-mee.com/movers-in-riyadh-company.html شركة نقل اثاث بالرياض http://emc-mee.com/transfer-furniture-jeddah.html شركة نقل عفش بجدة http://emc-mee.com/transfer-furniture-dammam.html شركة نقل عفش بالدمام http://emc-mee.com/transfer-furniture-almadina-almonawara.html شركة نقل عفش بالمدينة المنورة http://emc-mee.com/transfer-furniture-yanbu.html شركة نقل عفش بينبع http://emc-mee.com/transfer-furniture-taif.html شركة نقل عفش بالطائف http://emc-mee.com/transfer-furniture-mecca.html شركة نقل عفش بمكة http://emc-mee.com/transfer-furniture-qassim.html شركة نقل عفش بالقصيم http://emc-mee.com/transfer-furniture-khamis-mushait.html شركة نقل عفش بخميس مشيط http://emc-mee.com/transfer-furniture-tabuk.html شركة نقل عفش بتبوك http://emc-mee.com/transfer-furniture-alkharj.html شركة نقل عفش بالخرج http://emc-mee.com/transfer-furniture-abha.html شركة نقل عفش بابها http://emc-mee.com/transfer-furniture-buraydah.html شركة نقل عفش ببريدة http://emc-mee.com/transfer-furniture-najran.html شركة نقل عفش بنجران http://emc-mee.com/transfer-furniture-hail.html شركة نقل عفش بحائل http://emc-mee.com/transfer-furniture-dhahran.html شركة نقل عفش بالظهران http://emc-mee.com/transfer-furniture-kuwait.html شركة نقل عفش بالكويت http://emc-mee.com/ http://emc-mee.com/blog.html شركات نقل العفش Samar Ali · 10 months, 4 weeks ago

Log in to reply

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/ Samar Ali · 10 months, 4 weeks ago

Log in to reply

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 Smsma Ali · 10 months, 4 weeks ago

Log in to reply

شركة نقل اثاث بالدمام التفاؤل شركة نقل اثاث بالخبر كما انها افضل شركة نقل اثاث بالجبيل نقل عفش واثاث بالجبيل والخبر والقطيف والدمام http://www.tfa2ol.com/naklasas.html شركة نقل اثاث بالدمام http://www.tfa2ol.com/naklafsh.html شركة نقل اثاث بالجبيل Smsma Ali · 10 months, 4 weeks ago

Log in to reply

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 Smsma Ali · 10 months, 4 weeks ago

Log in to reply

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 Smsma Ali · 10 months, 4 weeks ago

Log in to reply

الشرق الاوسط افضل شركة نقل عفش بالدمام شركة نقل عفش بالخبر شركة نقل عفش بالجبيل شركة نقل عفش بالقطيف تنظيف كنب بالدمام تنظيف كنب بالخبر http://goo.gl/iAJsRz شركة نقل اثاث بالدمام http://goo.gl/qga5YC http://goo.gl/Vv4Sp9 http://goo.gl/52zZFy
http://goo.gl/VgTwlW http://goo.gl/SHZHnV http://goo.gl/1SwlvF http://goo.gl/1kXTpJ http://goo.gl/DuLCNP http://goo.gl/iksDnr http://goo.gl/Etnu4A http://goo.gl/x3BKPU http://goo.gl/hAu2Pm http://goo.gl/4XVcnD http://goo.gl/QkRQkZ شركة تنظيف كنب بالدمام http://goo.gl/7VW8I5 http://goo.gl/3NkrF1 http://goo.gl/BZTlLb http://www.east-eldmam.com/2015/10/06/sofas-cleaning-company-in-dammam/ شركة تنظيف كنب بالدمام http://www.east-eldmam.com/2016/04/27/cleaning-carpeting-and-carpet-company-in-dammam/ تنظيف موكيت بالدمام http://goo.gl/Nw25w7 شركة نظافة بالدمام Smsma Ali · 10 months, 4 weeks ago

Log in to reply

Packers and Movers Mumbai go to:- http://www.movers5th.in/packers-and-movers-mumbai/ Packers and Movers Delhi go to:- http://www.movers5th.in/packers-and-movers-delhi/ Packers and Movers Gurgaon go to:- http://www.movers5th.in/packers-and-movers-gurgaon/ Ravi Vaghel · 11 months, 2 weeks ago

Log in to reply

Packers and Movers Hyderabad go to:- http://www.movers5th.in/packers-and-movers-hyderabad/ Packers and Movers Bangalore go to:- http://www.movers5th.in/packers-and-movers-bangalore/ Packers and Movers Pune go to:- http://www.movers5th.in/packers-and-movers-pune/ Ravi Vaghel · 11 months, 2 weeks ago

Log in to reply

For Professional and Experienced Packers and Movers in Bangalore.Visit:- http://www.hirenmove.in/packers-and-movers/bangalore.html For Professional and Experienced Packers and Movers in Pune.Visit:- http://www.hirenmove.in/packers-and-movers/pune.html For Professional and Experienced Packers and Movers in Hyderabad.Visit:- http://www.hirenmove.in/packers-and-movers/hyderabad.html For Professional and Experienced Packers and Movers in Mumbai.Visit:- http://www.hirenmove.in/packers-and-movers/mumbai.html For Professional and Experienced Packers and Movers in Gurgaon.Visit:- http://www.hirenmove.in/packers-and-movers/gurgaon.html Suraj Baba · 1 year ago

Log in to reply

For Professional and Experienced Packers and Movers in Faridabad.Visit:- http://www.moveby5th.in/packers-and-movers-faridabad.html For Professional and Experienced Packers and Movers in Thane.Visit:- http://www.moveby5th.in/packers-and-movers-thane.html For Professional and Experienced Packers and Movers in Navi Mumbai.Visit:- http://www.moveby5th.in/packers-and-movers-navimumbai.html Suraj Baba · 1 year ago

Log in to reply

For Professional and Experienced Packers and Movers in Chennai.Visit:- http://www.moveby5th.in/packers-and-movers-chennai.html For Professional and Experienced Packers and Movers in Noida.Visit:- http://www.moveby5th.in/packers-and-movers-noida.html For Professional and Experienced Packers and Movers in Ghaziabad.Visit:- http://www.moveby5th.in/packers-and-movers-ghaziabad.html Suraj Baba · 1 year ago

Log in to reply

For Professional and Experienced Packers and Movers in Mumbai.Visit:- http://www.moveby5th.in/packers-and-movers-mumbai.html For Professional and Experienced Packers and Movers in Gurgaon.Visit:- http://www.moveby5th.in/packers-and-movers-gurgaon.html For Professional and Experienced Packers and Movers in Delhi.Visit:- http://www.moveby5th.in/packers-and-movers-delhi.html Suraj Baba · 1 year ago

Log in to reply

For Professional and Experienced Packers and Movers in Pune.Visit:- http://www.moveby5th.in/packers-and-movers-pune.html For Professional and Experienced Packers and Movers in Bangalore.Visit:- http://www.moveby5th.in/packers-and-movers-bangalore.html For Professional and Experienced Packers and Movers in Hyderabad.Visit:- http://www.moveby5th.in/packers-and-movers-hyderabad.html Suraj Baba · 1 year ago

Log in to reply

http://www.expert5th.in/packers-and-movers-pune/ Akash Singh · 1 year, 1 month ago

Log in to reply

For Relocation services in Noida visit http://www.expert5th.in/packers-and-movers-noida/ For Relocation services in Chennai visit http://www.expert5th.in/packers-and-movers-chennai/ For Relocation services in Thane visit http://www.expert5th.in/packers-and-movers-thane/ For Relocation services in Navi Mumbai visit http://www.expert5th.in/packers-and-movers-navimumbai/ For Relocation services in Faridabad visit http://www.expert5th.in/packers-and-movers-faridabad/ For Relocation services in Ghaziabad visit http://www.expert5th.in/packers-and-movers-ghaziabad/ Surya Pandey · 1 year, 1 month ago

Log in to reply

For Relocation services in Gurgaon visit http://www.expert5th.in/packers-and-movers-gurgaon/ For Relocation services in Mumbai visit
http://www.expert5th.in/packers-and-movers-mumbai/ For Relocation services in Delhi visit http://www.expert5th.in/packers-and-movers-delhi/ Surya Pandey · 1 year, 1 month ago

Log in to reply

For Relocation services in Pune visit http://www.expert5th.in/packers-and-movers-pune/ For Relocation services in Hyderabad visit http://www.expert5th.in/packers-and-movers-hyderabad/ For Relocation services in Bangalore visit http://www.expert5th.in/packers-and-movers-bangalore/ Surya Pandey · 1 year, 1 month ago

Log in to reply

Thanks for all your information.Website is very nice and informative content. http://www.dteller.in/packers-and-movers-hyderabad/
http://www.dteller.in/packers-and-movers-bangalore/
http://www.dteller.in/packers-and-movers-pune/
http://www.dteller.in/packers-and-movers-delhi/ http://www.dteller.in/packers-and-movers-gurgaon/ http://www.dteller.in/packers-and-movers-mumbai/ http://dteller.in/ Vinod Singh · 1 year, 7 months ago

Log in to reply

This article is really fantastic and thanks for sharing the valuable post. http://www.expert5th.in/packers-and-movers-pune/ http://packersmoverspune.top3rd.in/ Dinesh Kumar · 1 year, 9 months ago

Log in to reply

Thanks for all your information.Website is very nice and informative content. http://www.smaart5th.in/packers-and-movers-in-mumbai/ http://www.smaart5th.in/packers-and-movers-in-delhi/ http://www.smaart5th.in/packers-and-movers-in-gurgaon/ http://www.smaart5th.in/packers-and-movers-in-chennai/ http://www.smaart5th.in/ Dinesh Kumar · 1 year, 9 months ago

Log in to reply

This article is really fantastic and thanks for sharing the valuable post. http://www.smaart5th.in/packers-and-movers-in-hyderabad/ http://www.smaart5th.in/packers-and-movers-in-bangalore/ http://www.smaart5th.in/packers-and-movers-in-pune/ http://www.smaart5th.in/ Dinesh Kumar · 1 year, 9 months ago

Log in to reply

Thanks for all your information, Website is very nice and informative content. If you are looking Best Packers and Movers so Visit at : http://www.smaart5th.in/packers-and-movers-in-navimumbai/ http://www.smaart5th.in/packers-and-movers-in-thane/ http://www.smaart5th.in/packers-and-movers-in-noida/ http://www.smaart5th.in/ Panchu Kumar · 1 year, 10 months ago

Log in to reply

Thanks for all your information.Website is very nice and informative content. http://www.smaart5th.in/packers-and-movers-in-mumbai/ http://www.smaart5th.in/packers-and-movers-in-delhi/ http://www.smaart5th.in/packers-and-movers-in-gurgaon/ http://www.smaart5th.in/packers-and-movers-in-pune/ Panchu Kumar · 1 year, 10 months ago

Log in to reply

This article is really fantastic and thanks for sharing the valuable post. http://www.smaart5th.in/packers-and-movers-in-hyderabad/ http://www.smaart5th.in/packers-and-movers-in-bangalore/ http://www.smaart5th.in/packers-and-movers-in-chennai/ Panchu Kumar · 1 year, 10 months ago

Log in to reply

Thanks for all your information, Website is very nice and informative content. http://www.expert5th.in/packers-and-movers-noida/ http://www.expert5th.in/packers-and-movers-thane/ http://www.expert5th.in/packers-and-movers-navimumbai/ http://www.expert5th.in/packers-and-movers-ghaziabad/ http://www.expert5th.in/packers-and-movers-faridabad/ Aniket Kumar · 1 year, 10 months ago

Log in to reply

This article is really fantastic and thanks for sharing the valuable post. http://www.expert5th.in/packers-and-movers-delhi/ http://www.expert5th.in/packers-and-movers-bangalore/ http://www.expert5th.in/packers-and-movers-gurgaon/ http://www.expert5th.in/packers-and-movers-pune/ Aniket Kumar · 1 year, 10 months ago

Log in to reply

Thanks for post this helpful post - Please visit for More information about - http://www.expert5th.in/packers-and-movers-hyderabad/ http://packersmoverspune.top3rd.in/ http://www.expert5th.in/packers-and-movers-mumbai/ http://www.expert5th.in/packers-and-movers-chennai/ Aniket Kumar · 1 year, 10 months ago

Log in to reply

You want research ideas about the research paper. The is help you for your reasearch paper. Please go to official web site and get more tips about your research papers .

http://www.writeversity.com/about_us.php Nancy Mann · 2 years, 2 months ago

Log in to reply

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 Նարեկ Գալստեան · 2 years, 8 months ago

Log in to reply

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) Lucian Schulte · 4 years ago

Log in to reply

Think about what you like most in the IB syllabus. Yomna Abdelkader · 4 years ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...