Searching for the Lone Number
No matter what level of puzzle you are attempting to solve there are a few strategies that will allow you to get to a solution more quickly. The key strategy is to look for the lone number. In the following example, all the options for region 5 have been penciled in. At first there appear to be three places for the number 1 to go, but look between the 8 and the 3. There is a lone number 1.
It was not otherwise obvious that the only cell for the number 1 was row 6, column 5, as there is no number 1 in the immediate vicinity. Checking the adjacent regions and relevant row and column would not provide an immediate answer either – but no other number can go in that region.
While the example uses pencil marks to illustrate the rule, more experienced solvers are quite capable of doing this in their head. Remember that this principle is true for regions, rows, and columns: If there is only one place for a number to go, then it is true for that region, and also the row and column it is in. You can eliminate all the other pencilled 1’s in the region, row, and column.
Twins
Why limit yourself to one when sometimes two can do the job? In Sudoku you can easily become blind to the obvious. You might look at a region and think that there is no way of proving a number because it could go in more than one cell, but there are times when the answer is staring you right in the face. Sometimes the more obvious ways to find a solution is by looking at the obvious. Some solvers start by taking a few minutes to understand where the “givens” in the puzzle are laid out before they start to take any sort of solving action. This gives them a good feel for how easy or hard the puzzle is going to be so that they can apply certain strategies to their solving technique.
Take the following Sudoku:
It is an example of a “easy” puzzle. A good start as already been made in finding the obvious numbers, but having just solved the 9 in region 4 you might be thinking about solving the 9 in region 1. It seems impossible, with just a 9 in row 1 and another in column 2 that immediately affect region 1.
But look more carefully and you will see that the 9 in row 8 precludes any 9 in row 8 of region 7. In addition, the 9 in column 2 eliminates the cell to the right of the 4 in that region, leaving just the two cells above and below the 2 in region 7 available for the 9. You have found a twin. Pencil in these 9’s. While you don’t know which of these two will end up as 9 in this region, what you do know is that the 9 has to be in column 3. Therefore, a 9 cannot go in column 3 of region 1, leaving it the one available cell in column 1.
Triplets
In the previous example, having the “twins” did just as well as a solved number in helping you to find your number. But if two unsolved cells can help you on your way, three “solved” numbers together certainly can. All you need is to understand the concept behind looking for triplets. Look at the next example:
Take a look at the sequence 2-8-1 in row 8. It can help you solve the 7 in region 8. The 7’s in columns 5 and 6 place the 7’s in region 8 at either 8,4 or 9,4. It is the 7 in row 7 that will provide you with sufficient clues to make a choice. Because there can be no more 7’s in row 7, the 2-8-1 in row 8 forces the 7 in region 7 to be in row 9. Although you don’t know which cell it will be in, the unsolved trio will prove that no more 7’s will go in row 9, putting the 7 in region 8 at row 8. A solved row or column of three cells in a region is good news. Try the same trick with the 3-8-6 in row 2 to see if this triplet helps to solve any more of the puzzle.
Continue to Chapter 8...
