Sudoku (Number Place) is a puzzle game that is currently driving Britain crazy.
Here is an easy one.
Here is a difficult one.
Here is a Wikipedia article.
In technical terms, this is a "partial Latin Squares" problem. There are mathematical connections to experimental design, cryptology, and graph theory, to name a few.
There are many unsolved math problems associated with this puzzle - e.g. how many possible arrangements are there, characterize minimal given number patterns that lead to unique solutions, characterize given number patterns that do not have unique solutions, and so on.