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There are two ways to approach the Sudoku Solving process. You can use logic retaining in your memory the possible candidates for each cell, row, column, and region or you can write the candidates down.
I prefer to use the process of elimination to solve Sudoku. This leads me to my first of several Sudoku tips and that is pencil in all the possible candidates for each cell, row, column, and region.
Some Sudoku computer programs have the option to show you all the possible candidates. Some online puzzles allow you to pencil in your candidates. This makes life a little easier. The paper version, board games, and handhelds usually lack this capability. In these cases use my free
blank grid with candidates worksheet.
Naked Single Candidates
Every Sudoku puzzle will have cells that have only one possible candidate. If there aren't any other candidates showing, Sudoku players call this a naked single.
Every naked single allows us to safely eliminate that number from all other cells in the row, column, and region that the naked single lies in. The logic is simple. If there is only one cell a number can go in, then it can't go anywhere else. Below is an example of a naked single.
In the example to the left, you can see the naked single is the nine. All the other nines may be crossed off leaving a 6,8 pair, 6,7 pair, a single 7, and a 4,6,8 triple. If you didn't pencil in all the possible candidates, the naked nine would be less obvious.
No doubt you also noted in this example that once you solved for the naked nine, the 7,9 pair's solution became a naked single. The 7,9 pair is called a hidden single. Below is another example of a hidden single.
Hidden Singles
In the example at the left there are two hidden singles. Hidden singles have only one place they can go. The extra candidates in the cell "hide" the single solution. In this example, the third cell from the top is a seven. Likewise in the bottom cell the only number that can go there is a four.
When there is a lot of candidates showing from the surrounding rows, columns, and regions, a hidden single can be hard to spot. Hidden singles will occur often.
Now for my next Sudoku tip. Look for "naked pairs".
Naked Pairs
In the example to the left there is a "naked pair". A naked pair is two identical candidates in a particular row, column, or region. This combination of candidates will occur often also. When you see a naked pair, it is safe to eliminate those two numbers from all other cells in the row, column, or region the pair reside in.
In the naked pair example it is safe to eliminate the four and six from the two quads of 3,4,6, and 8. Doing so, leaves two 3,8 pairs. The 3,4,6, and 8 quads are really "hidden pairs". More Sudoku tips on this.
Hidden Pairs
In the example at the left there is a hidden pair 2 and 9. They are circled in red. Hidden pairs are identified by the fact that a pair of numbers occur in only two cells of a row, column, or region. They are "hidden" because the other numbers in the two cells make their presence harder to spot.It is safe to remove all other digits from the two cells circled in red so that only the two and nine remain. Hidden pairs will appear often in your Sudoku puzzles and games.
Naked Triples
Another Sudoku tip is to look for "naked triples". Naked triples like the name suggests are three numbers that do not have any other numbers residing in the cells with them. Unlike naked pairs, naked triples do not need all of the three candidates in every cell. Quite often only two of the three candidates will be shown.
In the example at the left, the three cells circled are the three naked triples. They are 5,6 and 9. Only a 5,6 and 9 can appear in those three locations. Therefore, you can remove all 5,6, and 9s from the other cells in this row.
When you remove the 6,9 from two cells and the 5,6 you will discover a naked pair (1,4) and a hidden single (2). See how these Sudoku tips help you solve puzzles?
Hidden Triples
Hidden triples are much harder to spot. They will occur in harder puzzles. Hidden triples like naked triples are restricted to three cells in a row, column, or region. Hidden triples like hidden pairs have additional digits that camouflage the three candidates.If you look at the example at the left, you will see three cells circled in red. These are the hidden triples. Can you spot them?
You are right, they are 4, 8, and 9. Remove the extra numbers from the cells circled in red. Do you think hidden triples are tough to find? Try quads.
Naked Quads
Another Sudoku tip is to look for "naked quads". Naked quads are like naked triples with the exception that four numbers are restricted to four cells in a row, column, or region. In the example at the left the naked quads are circled. They are 3,5,6, and 8. Remove any instance of these four numbers from the other cells in this row.
Hidden Quads
The last of my Sudoku tips for this article is to look for hidden quads. As the name suggest, hidden quads are four numbers that are restricted to four cells in a row, column, or region. These four numbers are hidden by additional candidates. Hidden quads are very difficult to find. The good news is I have rarely seen them. (Maybe because they are hidden so well!) They occur only in a few of the more difficult puzzles.
In my example at the left, the hidden quads circled in red are 1,5,6, and 8. It is safe to remove the extra digits (3,4,7,9) from these four cells.
I hope these Sudoku tips will help you in your quest to become a professional Sudoku puzzle solver.
Learn the Sudoku X-Wing to solve some tough puzzles.
Learn the Sudoku XY-Wing to solve more tough puzzles.
Learn the Sudoku Swordfish pattern to solve some tougher puzzles.
Try this brain teaser to solve some difficult puzzles.
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