GoldyOrNugget
Señor Member
- Joined
- Jul 14, 2012
- Messages
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- HSC
- 2012
Re: HSC 2013 4U Marathon
The answer is 105/7 = 15. You don't have to use cases -- you can prove that for any of these bead strings, none of its rotations will be identical to itself, so there's no risk of double counting: 7!/(4!*2!*1!) will count every rotation precisely 7 times.
For the record: ['ggrggyr', 'gggrgyr', 'ggrggry', 'ggggyrr', 'ggrgygr', 'gggrygr', 'gggrrgy', 'ggggrry', 'ggrrggy', 'ggggryr', 'gggrgry', 'ggrgrgy', 'gggyrgr', 'gggygrr', 'ggygrgr']
Nup. It's a circle, and also I think you have to use cases.
The answer is 105/7 = 15. You don't have to use cases -- you can prove that for any of these bead strings, none of its rotations will be identical to itself, so there's no risk of double counting: 7!/(4!*2!*1!) will count every rotation precisely 7 times.
For the record: ['ggrggyr', 'gggrgyr', 'ggrggry', 'ggggyrr', 'ggrgygr', 'gggrygr', 'gggrrgy', 'ggggrry', 'ggrrggy', 'ggggryr', 'gggrgry', 'ggrgrgy', 'gggyrgr', 'gggygrr', 'ggygrgr']