# When logic problems require "yes-no" questions, are there conventions for questions that might get an "I don't know"?

A common constraint in logic problems is the one restricting questions you may ask to those that can only be helpfully answered with a "yes" or "no".

But in some cases, you might ask someone a question where "yes" or "no" are the only answers if you know the answer, but where some respondents may lack the necessary information to know.

Example: You meet one "truth-teller" and one "random-respondent", who is "50-50" to reply yes or no to any given question. You don't know who's who, but they do. If you're limited to "yes/no" questions, can you ask one of them what the other person would say? (The problem is that the truth-teller doesn't know, and knows he doesn't know; his only possible honest answer is "I don't know."

What, if anything are the conventions in cases where "yes/no" is a constraint, but the issue of questions the respondent can't answer is not explicitly addressed? Presumably, they must fall into one of the following:

1. You're not allowed to ask a question where the respondent might not be able to reply. This is simple, but... seems somehow more odd to me than the other arbitrary ridiculous rules, although I have no idea why that is.
2. You are allowed to ask questions like that, in which case, you must also assume they are allowed to convey "I don't know" (assume they have a veracity type that would make them honest).

I was deliberately using a simple example, but the puzzle that this comment is on is what inspired the question. (I haven't solved it yet, so please don't share whether it's relevant to that particular solution; I'm more interested in what assumptions, if any are generally applied to other problems like this.

• More rigorously speaking, what I think you're looking at is whether a set of inputs fully determines the outputs, without knowing what the inputs are. If it does, you know, and if it doesn't, you don't know. For instance, if I asked "I tell you the first, second, and third byte of a three-byte number. Do you know the number?" you'd say 'yes.' If I asked you to tell me what it is, you'd say 'no clue.'
– user20
Apr 20, 2015 at 17:58
• I would suggest that the simplest resolution is probably to have puzzles simply prohibit head-exploding questions. Alternatively, they could specify that anyone answering a question is entitled to regard the answer as being 'yes' if they have no reason to believe it less truthful than a 'no' response, and vice versa; if to the best of the answerer's knowledge either answer would be equally truthful, the answerer may answer in whatever fashion would be most vexatious. Apr 30, 2015 at 22:48