I'd preface the solution and the key point before mentioning that I'd seen this problem before and then further ask if they still want me to code up the solution. This eliminates the case that I, the interviewee might be bluffing. Also they might just be interested to know if you can think on your feet by then adding a twist later. who knows not my call.

It would be dumb if the next one they throw at me is one i've also seen or is ridiculously hard for an interview. Then i'd question the value of my honesty.

The interviewer might also just be a cog in the machine and know how it works.

"Just solve it and I'll note down an A+" is sometimes better than "candidate was honest, but didn't finish the alternative riddle."