I actually do what you suggest. I pick problems I've never did before and try to solve it in less than 1/3rd the time I allot for the interviewee to account for

I actually do what you suggest. I pick problems I've never did before and try to solve it in less than 1/3rd the time I allot for the interviewee to account for interview time pressure. Even then there are probably biases because I pick problems that I can solve so I periodically review the candidate success rates on problems and change them out if they are too simple or too complex.