What was a project or spec that got put on your desk that could not possibly be done? How did you explain the dilemma to the requester? More importantly, did they understand after you explained the fundamental issue? 
Best (worst) logically impossible task assigned to you?
project management;communication
I was told to make the printer print faster.Serious, and I was written up for failing. The boss wasn't very tech savvy and didn't understand why I couldn't speed it up. 