Ben, full disclosure: you should check the most recent edits on that wiki article. I’ve done a bit of cleaning up there. Which is to say, the wiki article is likely to be exactly as right as my contributions to this conversation (which I am not at all sure are right).
James, I still think what you’re doing only expands the possible solution set. Otherwise, you’re claiming that, by providing one way that they could solve the puzzle without reference to the colors they can see (i.e. your color chart scenario), you’ve proved that there are always at least two solutions to the problem. That claim is every bit as broad as the claim that in a given circumstance, X is the only way to reason out of the problem. It seems clear that if it’s possible to come up with a solution case where there is only one way to reason from it, then that is a legitimate solution the problem, and one the Master could set up. Your claim is a general claim: no such solution exists. You have not proven that (indeed, your argument looks a lot like you’re saying, “‘it’s evident’ that some other algorithm will always exist”).
You have likened your criticism of this problem to the Blue Eye problem, but the big difference here, and why I think your criticism here is well placed, is that here the puzzle is inherently uncertain: we don’t know how many logicians there are or how many colors of headband there are, so the solutions we offer are general, e.g. the problem can be solved if there are three logicians, one with a red, one with a yellow, and one with a blue headband (or is that blue, magenta, and cyan?). We need to assume some facts to make the problem solvable, so we can question which assumptions are legitimate and why, e.g., is it any more legitimate to assume that there are two of each headband than to assume that every logician knows about the the color chart.
Phoneutria, do you reject the idea that there are other solutions to the problem besides the everyone-can-see-their-color (ECSTC) solution? Do you have grounds other than Occam’s Razor for preferring the assumption in the ECSTC case?