Not everyone who asks these problems is an idiot. Given the amount of dick-swinging that goes on from Google employees and the famed interviews one gets from the big tech companies I can imagine a lot of younger managers reading these and thinking that it's how you get hold of great engineers. The simple fact is that a lot of the time interviewers aren't experienced at interviewing, and most of them will spend longer formulating a process than an interviewee will spend preparing for said interview.
Anyway, surely the ideal thing to do would be to play along with the interview, answer the stupid question as best as you can and when the interviewer ends with "any questions for us?" you ask them why the felt it was necessary to test you on a general-purpose brainteaser with no relevance to the job when they could have asked something more relevant, like "x". This way you show that you roughly know what you're doing, you're aware of how the interview went and you've provided a question that will make people sit up and think.
Anyway, surely the ideal thing to do would be to play along with the interview, answer the stupid question as best as you can and when the interviewer ends with "any questions for us?" you ask them why the felt it was necessary to test you on a general-purpose brainteaser with no relevance to the job when they could have asked something more relevant, like "x". This way you show that you roughly know what you're doing, you're aware of how the interview went and you've provided a question that will make people sit up and think.