How he solves the problem doesn’t matter. You don’t care in the interview if he had the answer memorized or if he fumbles through it.
I do not want to work with anyone who finds that getting their hands dirty is beneath them. It is very, very rarely going to be a good use of their time to do those problems. It will often be a good use of their time to teach those problems. A senior engineer, even one who’s unlikely to work with junior engineers on a regular basis, will need to explain their thinking. They need to show humility and compassion. Those are practiced attributes. This precise situation is the best practice you can get - New and Unknown person, some amount of challenge and complexity involved.
Thinking that whiteboarding problems are a bad use of time is a very strong signal for a senior person who is out of touch.
At an old job, my boss was moving desks and he came across an extra copy of CLR "Introduction to Algorithms" and he asked if anyone wanted it. As he was my direct supervisor, he said he'd give it to me only if I promised never to open it, and only to use it as a monitor stand.
I do not want to work with anyone who finds that getting their hands dirty is beneath them. It is very, very rarely going to be a good use of their time to do those problems. It will often be a good use of their time to teach those problems. A senior engineer, even one who’s unlikely to work with junior engineers on a regular basis, will need to explain their thinking. They need to show humility and compassion. Those are practiced attributes. This precise situation is the best practice you can get - New and Unknown person, some amount of challenge and complexity involved.
Thinking that whiteboarding problems are a bad use of time is a very strong signal for a senior person who is out of touch.