What if the teacher writes the test day on a piece of paper at the beginning of the week and hides it in his desk? That way "we won't have the test at all" is no longer a possibility.

I think that gets you back to impossible instructions—if the teacher had written "Friday", then on Friday the students wouldn't be surprised by the test on Friday. I guess, unless the students think it's possible the teacher left it blank or wrote "No Test This Week" or something on it?