Find Twins and Triplets
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 an “easy” puzzle. A good start has already been made in finding the obvious numbers.
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 region 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 region 7, 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.
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.
