Sudoku grid consists of 81 squares divided into nine columns marked a through i, and nine rows marked 1 through 9. The grid is also divided into nine 3x3 sub-grids named boxes which are marked box 1 through box 9.
Scanning techniques
The easiest way starting a Sudoku puzzle is to scan rows and columns within each triple-box area, eliminating numbers or squares and finding situations where only a single number can fit into a single square. The scanning technique is fast and usually sufficient to solve easy puzzles all the way to the end. The scanning technique is also very useful for hard puzzles up to the point where no further progress can be made and more advanced solving techniques are required. Here are some ways of using scanning techniques:
1. Scanning in one direction:
In our first example we will focus on box 2, which like any other box in Sudoku must contain 9. Looking at box 1 and box 3 we can see there are already 9s in row 2 and in row 3, which excludes the two bottom rows of box 2 from having 9. This leaves square e1 as the only possible place into which 9 can fit in.
2. Scanning in two directions:
The same technique can be expanded by using information from perpendicular rows and columns. Let’s see where we can place 1 in box 3. In this example, row 1 and row 2 contain 1s, which leaves two empty squares in the bottom of box 3. However, square g4 also contains 1, so no additional 1 is allowed in column g. This means that square i3 is the only place left for 1.
3. Searching for Single Candidates:
Often only one number can be in a square because the remaining eight are already used in the relevant row, column and box. Taking a careful look at square b4 we can see that 3, 4, 7 and 8 are already used in the same box, 1 and 6 are used in the same row, and 5 and 9 are used in the same column. Eliminating all the above numbers leaves 2 as the single candidate for square b4.
4. Eliminating numbers from rows, columns and boxes:
There are more complex ways to find numbers by using the process of elimination. In this example the 1 in square c8 implies that either square e7 or square e9 must contain 1. Whichever the case may be, the 1 of column e is in box 8 and it is therefore not possible to have 1 in the centre column of box 2. So the only square left for 1 in box 2 is square d2.
5. Searching for missing numbers in rows and columns:
This method can be particularly useful when rows (and columns) are close to completion. Let’s take a look at row 6. Seven of the nine squares contain the numbers 1, 2, 3, 4, 5, 8 and 9, which means that 6 and 7 are missing. However, 6 cannot be in square h6 because there is already 6 in that column. Therefore the 6 must be in square b6.
