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Claudia wants to use 8 indistinguishable red beads and 32 indistinguishable blue beads to make a necklace such that there are at least 2 blue beads between any red beads. In how many ways can she do this? This is one of the unsolved problem in the book 'A Path to Combinatorics for Undergraduates' by Titu Andreescu and Zuming Feng. My approach: Denote blue by b, red by r. Then we create elements of the form 'brb'(8 elements), and 16'b's. We place the 16 'b's arounds a circle with a space in between them and we choose from those 16 available places 8 for the 'brb' and divide the whole be 2 to account for rotational symmetry.

I am not sure whether I am fully accounting for the rotational symmetry and the fact that the beads are indistinguishable. Not Homework. Trying to learn. Thank you.

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    Look up Polyá Counting or Burnsides Lemma.2012-12-22
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    Okay I will but I was looking for something simple. I am only in high school.2012-12-22
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    Sorry - irrelevant - but I laughed a little. The book's called "A Path to Combinatorics for *Undergraduates*," it's natural that you'll receive undergraduate tools here, regardless of what level of schooling you're actually at. :)2012-12-22

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