I found that clearly defining and specifying a question is half way to the answer. More often than not, the questions are asked poorly and the desired goal is obscured confusingly.
For example the first question, "How do you map the list on the left to the list on the right?" Huh? What do you mean by "map"? Do you want a data structure to link the two? Are the list infinite? Or just upto 100? Do you want to derive the algorithm to produce the next number? Or do you want a function that given the left list produce the right list? Or do you want a function that given a number from the left list, produce the corresponding item on the right. On and on.
Or, in the context of an interview, thats also a skill on the part of interviewee, to ask these/similar questions that will help her/him get to the solution.
I find that slightly vague questions are actually helpful in interviews. In the real world, finding requirements and interpreting specs require these skills. So I will ask questions that can be understood a few ways to gauge the prospective hire's requirements gathering.
This can backfire, and requires a bit of fluidity in the interviewer's part -- no cargo cult questions, just open problem solving. In a really good case, me being open to what the interviewee was saying about ambiguity led to a fascinating attempt to solve a different problem than I had originally structured, but we found out we work well together and solved a fun problem. At the same time he showed me his skills, and I showed him my skills. Result: both of us decided working together would be beneficial -- the best possible outcome of an interview (although just as good would be mutually deciding we wouldn't work well together and amicably parting ways).
Indeed, though not as collaborative as your case, I've been intrigued by the variations of the original problem that evolved because of how both of us(candidate & me) probed the problem.
For example the first question, "How do you map the list on the left to the list on the right?" Huh? What do you mean by "map"? Do you want a data structure to link the two? Are the list infinite? Or just upto 100? Do you want to derive the algorithm to produce the next number? Or do you want a function that given the left list produce the right list? Or do you want a function that given a number from the left list, produce the corresponding item on the right. On and on.