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But if they haven't studied graphs and are unable to give you rigorous answers, will you forgive them because they haven't taken the right classes?

It seems to me you should ask questions you expect the candidate to be able to give good answers for, period.

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My philosophy is that you ask questions either a) to ensure someone knows material they say they do (if you claim you have a bunch of Java experience, you are expected to know how java.util.collections works or how the final operator works, as examples) or b) to see how someone thinks. The questions I ask sometimes truly do not have answers, but seeing the walls pop up and the candidate try to work around the walls tells me a lot about how they will approach problems in the workplace.

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