I'm amused by tales of 3 impossible questions in recent AS-level exams, but also by the quotes attributed to (the fairly generic) "students":
Students have complained that even if the questions are discounted, it is difficult to know how much the overall grade could have been affected by the time wasted trying to interpret a wrong question.
I remember being taught a fairly non-linear approach to exams - if questions are worth the same amount, do the easiest stuff first. It's not a question of whether the question is impossible or just difficult - it's a matter of point-scoring in an allotted time.
Which begs the question (another one) - should students deliberately get rewarded for creative approaches to exams? What if we encouraged more creativity through something more "engaging" than a simple list of questions with a bunch of possible answers?
In the real world, some tasks can be done, and some can't. Some can be done, but may take an inordinate amount of time. Some may require knowing other things first.
Working out how to approach a series of questions is often far more important than answering the questions themselves.
Maybe we actually need more impossible questions, not less.