This time, instead of looking for the correct number for a square, we're going to look for the correct square for a number. To do this, we're going to draw some lines. Take a look at box 6:
Box 6 needs a 4. Let's find out where it goes by eliminating all of the boxes where it can't go. There's a 4 in row 5, so we'll draw a line through that row. There's also a 4 in row 6 and columns 7 and 8. We'll draw lines through all of those.
Now there's only one open square in box 6 -- the square at 4,9. We've solved the 4.
Let's draw some more lines to find the location of the 6. We can strike through row 5, row 6 and column 9, leaving only one open square. We can put the 6 in the square at 4,8.
You now have all the knowledge you need to finish the puzzle yourself!
Using simple logic and the basic strategies we've discussed here, along with the thousands of other strategies out there developed by sudoku enthusiasts, you'll be able to solve just about any sudoku puzzle. As the difficulty increases, it'll just take you longer to solve each square because some squares won't be solvable until you've solved certain other squares -- sometimes until you've solved entire regions of the grid. As you work on more puzzles, you'll come up with your own approaches and strategies. It's all a matter of finding and cultivating your own sense of sudoku logic.
While sudoku is a game of logic, there are some puzzles that ultimately defy logic and require -- to the horror of many sudoku purists -- guessing.