[billygrippo]

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For there to be a unique solution there would have to be one and only one rule that predicted the first n numbers in the sequence correctly. But there is never only one such rule, there are always an indefinite number of rules that can fit or 'predict' the pattern, and which may all yield distinct answers (all equally 'correct') for what the next number is in the sequence.

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occam's [censored] razor!!! jesus [censored]!

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Those sorts of puzzles have nothing to do with Occam's razor. Occam's razor (say, adopt the theory that is most ontologically parsimonious) has to do with choosing between scientific theories that are equally empirically adequate. You simply gave a puzzle and asked for a solution.

Now we could invoke some principle like Occam's razor in our instructions for answering that sort of puzzle--like saying "give the simplest rule/formula that solves the problem," but that still does not mean there is a unique solution to the original puzzle--just one that we favor over others on grounds other than that it's an accurate solution.

I simply claimed there was no unique solution to those sorts of sequence puzzles, and that is true whether or not we decide to adopt some standard for choosing among equally adequate solutions in terms of simplicity of formula, or some such standard. But even in such a case you might be surprised at how difficult it is to provide an adequate philosophical defense of 'simplicity criteria.'

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very well put. however, try to solve the original puzzle. I assure you there is a "simple" answer, that stands out from the other possible soultions.