Distance Three Sudoku

Today I'm posting one of the very first puzzle variants I designed, and it is still one of my absolute favorites.  The rules of this puzzle are simple.  The clues reveal whether the distance between the numbers in those cells is less than, equal to, or greater than three.

If you notice how among the standard collection of numbers used in Sudoku, the numbers four, five and six each have exactly two numbers which are distance three apart, and how this partitions our set into exactly three groups, you can start seeing why three is a very special distance to consider. 

This is also one of the many puzzle types found in my new book: Math-Infused Sudoku.

  

Click here for a high quality PDF for printing.

For the solution click here.

For a small hint, highlight the following text:  The bottom left three-by-three square is determined by the 7 and its clues alone.  Thus that square can be completed without looking at the rest of the puzzle.  From there you can go on and fully complete the top and middle left squares, before considering the other six.