The most difficult questions are about some particular algorithms or mathematical problems that interviewer is very familiar with but the candidate has never heard of. Not only it may create a stressful situation (candidate thinks that it is something he/she is supposed to know), it is not how the people solve new problems in IT. Many people may not be able to fully understand a particular mathematical (e.g. theoretical) theorem in a matter of 10-15 minutes and without good understanding of that particular theorem it may be hard to apply it to the real-life problem presented by the interviewer. For example, the question about finding the majority number in a large input sequence.
