In the above example, you’ll see that the top left block has 3 open squares that could only be filled by a 2, 3, or 6. Additionally, we can eliminate the 2 as a potential candidate for the middle square, since there’s a 2 located in that same row. Even better, we can eliminate 6 on the right-most square, since there’s a 6 in that column. These eliminations will make this 3x3 even easier to solve in the future.
In this example, notice that 2, 5, and 9 are the potential candidates for the missing squares in the vertical column. We can also eliminate 5 from the middle square, since there is another 5 in that row already.
In this example, notice how the topmost row could only be filled by a 6, 7, or a 9. We can eliminate 7 from the middle square and 9 from the rightmost square, since these numbers are in the columns associated with those squares.
In the above example, we can see a hidden 3x3 in the 3rd vertical column from the left. The column is missing not only a 2, 5, and 9, but also a 6 and an 8. But since a 6 and an 8 could only fill the two top right squares in the bottom left block, we know that those 2 squares must be either a 6 or an 8. Therefore, we know that we’ve found a 3x3 in the remaining squares in the column—although there’s no 9 in the row that belongs to the top right square in the bottom left block, we can eliminate 9 as a potential number to fill that square, since it is a part of the 3x3.
In the above example, imagine that you’ve continued in the puzzle and managed to find the locations of the blue 5 and 9. With this information, you now know that the green square must be a 2.
In this example, since we know that the green square is a 2, we can deduce that the middle square of the 3x3 must be a 9. That leaves only 1 option for the final square of the 3x3: the 5 at the bottom.
Working on a Sudoku in pencil also makes it much easier to take notes as you go.
