interesting question that appears to cause a paradox at first.

Another paradoxes is:

A teacher wants to set a test thats a complete surprise.
IT can not be at the end or the start of the week because it's too predictable, so this limits the number of options to 3 days. The test can not be on thursday because it is the last day before the last day.

Working back, it can not be on any day. Yet if the teacher set the test on Friday, it would come as a complete surprise.... Weird...