Last night on the train ride home, I was thinking about the math of Sudoku. I was wondering what the minimum number of givens or clues (i.e. squares with specified numbers) you have to specify in order to have a unique solution. It turns out to be an open problem, with the smallest known limit as 17. According to Gordon Royle there are 35396 solutions with 17 givens.
If you think about it much, it is a really hard problem. What is a good way to represent it having a "unique solution"?