In some senses, many companies will want to know the same things about their possible future CEO that any company would want to know during any interview process.
Just as it's important to avoid clichés and meaningless buzzphrases when seeking out lower-level workers, the things you ask your executives will stick with them and make a difference. It's important to remember that just as you are judging future applicants, the people you interview are getting a glimpse of you in the way that you approach them.
This seems to be a topic of much discussion on the internet, and there are inevitably going to be differences as to the best way to go about this problem. Beauty CEO Jane Park, for example, writes in Inc. that there's "one question" interviewers need to ask: "How would you solve our biggest business challenge?"
Park's reasoning behind this is that this question will challenge the applicant and give the interviewer a real time demonstration of their thought processes in problematic situations. A point she doesn't mention is that this also reveals how seriously the candidate has done the research on your company to skillfully address whatever "your biggest challenge" may be.
But let's be practical about this: there's no magic question that will single out the right person. Rather, each company will have their own series of questions, priorities, and overall strategy necessary to sort through all those possible executives for the right one. An executive recruiter like YES Partners brings with them not a magic wand, but expertly honed knowledge that can be put to good use in your favor.
Finding people is easy, but finding the RIGHT people is not. YES Partners helps companies FIND the right people – for all company functions, across many industries and globally.