Come not between the dragon and his wrath. Apparently this is a quote from Shakespeare, and I happened to have seen this on a dragon notebook I bought from Waterstones.

I think this puzzle really is a system of simultaneous equations in disguise.

So buckle up my friends, and give this a go!

When you are ready, keep reading for the solution.

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Solution

Let’s say A = x. And given the sum of any three consecutive terms is 30, we can have

Ok so we have B in terms of x. Let’s apply this relation again to three other terms.

Oh so D is x. Hmm. Well if we continue applying this relation to later terms, we find the following relations.

Hey that’s what we need!

Did you get this right? And how did you approach this puzzle? Let me and others know in the comments!