Puzzles available online or in books often come with provided answers that are unsatisfactory in some way. The social aspect of Puzzling SE means it provides a good home for such questions to be re-asked (with correct attribution) if the published solution was unhelpfully terse, or worse, a multiple-choice answer only. The question asker here knows what the answer "should" be, can ask for particular attention to be given to the part they felt they didn't "get", and can reward (upvoting, green-ticking or even bounty-awarding) whatever answer provides the most illuminating explanation.
But what about cases where the published answer appears to be wrong — or suggests a lapse in logic during the construction of the puzzle, which may render it unsolvable? It's clearly important to acknowledge the possibility of the published answer being incorrect, or the puzzle unsolvable, when posting the puzzle as a a question here. What's less clear is:
- Should the OP provide, again with appropriate attribution, the published solution? If so, where? Should it be posted as part of the question, as a hint to the question, or (I think not, but it would have a certain logic) even posted as a self-answer to the question?
- Should the OP comment on what seems to be wrong with the published question and solution? If so, where?
- Should the OP go further, and provide their own attempt at a solution, or a "proof" as to why no solution is possible? If so, where?
- If the question receives conflicting answers — perhaps some agree with the provided answer and some do not — how is the OP to judge who's correct, given they suspect the published answer may not be definitive? (Role here for community input, via comments and up/down-voting.)
I've kept the above general, as that often makes Meta questions more helpful in the longer term, but obviously it's triggered by a particular example: False Logic Puzzles by Norman D. Willis (Sterling Publishing Company, 1997, ISBN: 978-0806998046). This book extends those "some islanders are truth-tellers, but the rest are liars" logic puzzles beloved of everyone from Epimenides some 2600 years ago, to Math Olympiad selection test writers today. It introduces further "standards of veracity", such as people who lie or speak truthfully in alternating statements, or who lie at random, or depending on the time of day, or even depending on the veracity standard of the person they are talking about. All good clean logical fun, until doubts start to sink in about some of the answers.
Much of the book is well done, with some entertaining puzzles. The wording is frustratingly sloppy at times — sometimes it's necessary to check the answers just to see how the question was supposed to be interpreted — but I could tighten up or reword those elements if reposting here. More troubling is what looks like sloppy logic in some of the solutions, for example apparently unjustified inferences. Then again, maybe my brain's just turned to mush while trying to reason out "if it's the morning, how can C be lying about A lying about B lying about what time of the day A lies?" (A genuine example by the way.) It doesn't seem to be a well-known book but a few online reviews like "I couldn't work out the answer to some of these" suggest I'm not alone in my confusion. If any of the Brains Trust here happen to know Willis's work (he was a prolific puzzle author, but has only once been referenced on this site before), you might advise me how likely the error is to be on my part or the writer's.
Having perused the answers to "unsolvable puzzles" on Meta, I can see one option that would let me salvage a solvable question from an apparently unsolvable one (without losing anything if it turns out the mistake is mine) would be to rephrase questions like "Which of A, B, and C are truth-tellers and which are liars?" to "Which, if any, of A, B, and C can we determine to be truth-tellers or liars?" This way, even if some of the identities turn out to be ambiguous, we still have a meaningful question... unless the problem with the puzzle's construction is so severe that no combination of liars and truth-tellers could produce the given collection of statements, and I don't think I've seen any that bad yet.
