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    <p>Calculating the number of possibilities here actually has an incredibly neat solution (in my opinion).</p> <p>Notice that for n notes, the number of possible connections ( <code>C(n)</code> ) if the first note is connected to the second is <code>C(n-2)</code>. Otherwise it is <code>C(n-1)</code>. This means that</p> <pre><code>C(n) = C(n-1) + C(n-2) C(1) = 3 //Either the first and second are connected, //neither are connected, or the end is connected. C(0) = 2 //Either the end is connected or it isn't </code></pre> <p><strong>Note:</strong> If the last note in a single note example can be connected "to itself" G(0) is 1 Otherwise, it is 0. In addition I am unclear whether <code>E-E</code> and <code>E E-</code> are separate, if they aren't then, <code>C(1)</code> is 2 not 3. Note these only apply for sequences of 0 or 1 <strong>on their own</strong> you'd have to have an if statement outside of the actual function <code>C(n)</code> to return 1 instead of 2. Otherwise it screws up the whole recurrence. A bit messy, but that's the nature of real world data in algorithms</p> <p>This means you've basically got a variant on the fibonacci series! Cool right? </p> <p><strong>Data Representation</strong></p> <p>I would have a list of n <code>boolean</code>s. An array would work fine. If 2 notes are connected, then that entry in the array should be <code>true</code>. I would have index 0 be the connection be the first and second notes, and index <code>n-1</code> be whether or not the last note is connected to anything.</p> <p><strong>Permutation Generation</strong></p> <p>The way in which we calculate the total number of possibilities lends itself nicely to a generation method (<code>G(n)</code>). For n we need to tack on <code>E-E</code> to <code>G(n-2)</code> and <code>E</code> to <code>G(n-1)</code>.</p> <p>At the base of this recurrence we have:</p> <pre><code>G(0) = {E, E-} G(1) = {E-E, E E, E E-} </code></pre>
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    1. COI guess that is an ambiguity, Can the last not be linked to itself? If so `G(0)` is 1 otherwise it's 0. Thanks I'll edit to specify this
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    2. COwell, the way i read the problem is that those 12 elements are actually in a circular buffer and only 2 non connected adiacent elements can actually be connected. So i guess that your solution doesn't generate these but i guess i misread the solution when i said that G(1) is wrong
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    3. COHm I'm reading this from the context of musical notes, in which case I believe my edits cover everything necessary
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