|There will be cake today|
Unless... there is one problem when the process is viewed from a logical perspective.
Consider me having made a cake and planning to bring it in on Friday. Friday is the last workday in the week, so the others could predict the cake to be brought on Friday as soon as they see on Thursday that there is no cake. So I will not choose Friday, because it won't be a surprise on that day.
However, assuming totally logical actors, also Thursday is not an option, since the others will come to the same conclusion that Friday is off the list and they would know on Wednesday evening, when no cake appeared so far, that I will bring it on Thursday. So Thursday is not a surprise day either. We can iterate this argument and end up with the interesting situtation that I have to bring the cake on Monday, since all other days would not be a surprise. Having decided that even Monday is no surprise either.
So it looks like that it is impossible to bring a cake on a weekday as a surprise if everybody knows that I have to bring a cake within this week.
The paradox is interesting but it is also obvious that there is a difference between totally logical and natural actors. Asking people, they usually agree on the argument that Friday would be no surprise, but every other day would be. What do you think?
If you like this kind of puzzles, I recommend the book of Zbigniew Michalewicz and his son on Puzzle-Based Learning.