For more information or to change your preferences at any time go to the Cookie Policy. Cookies are small pieces of text sent to your web browser that assist us in providing our Services according to the purposes described. A cookie file is stored in your web browser and allows our Services or a third-party to recognize you and make your next visit easier and the Service more useful to you.
Some of the purposes for which Cookies are installed may also require the User's consent. Cookies can be "persistent" or "session" cookies.
Persistent cookies remain on your personal computer or mobile device when you go offline, while session cookies are deleted as soon as you close your web browser. Functional cookies are set to recognise you when you return to our Website, set up your consent settings, and embed functionality from third party services. Also, these cookies enable us to personalise our content for you and remember your last game progress.
These cookies are necessary for the functionality of the Website. You may set your browser to block these cookies, but the Website will not function properly without them. We may use analytics cookies to track information on how the Website is used so that we can make improvements.
We may also use analytics cookies to test new advertisements, pages, features or new functionality of the Website to see how our users react to them. These types of cookies and other storage technologies such as Pixel Tags are used to deliver advertisements on and through the Service and track the performance of these advertisements. Do one at a time until you can plot one more number into a cell. Then, start with the basic techniques again, and repeat the process. You should be able to solve almost any Sudoku puzzle using these techniques.
Techniques for removing numbers: Sole Candidate When a specific cell can only contain a single number, that number is a "sole candidate". This happens whenever all other numbers but the candidate number exists in either the current block, column or row.
In this example, the red cell can only contain the number 5, as the other eight numbers have all been used in the related block, column and row. Unique Candidate You know that each block, row and column on a Sudoku board must contain every number between 1 and 9. This example illustrates the number 4 as the unique candidate for the cell marked in red. The example shows that the number 7 can only be inserted in the red cells of the middle row. Thus you can remove 7 as a possible candidate from the rest of the row.
In the middle and the middle-left blocks, the number 8 must be placed in one of the red cells. This means, we can eliminate 8 from the upper and lower rows in the middle-right column. Naked Subset The example shows that row number 1 and row number 5 both have a cell in the same column containing only the candidate numbers 4 and 7. These two numbers appear as candidates in all of the other open cells in that column too, but since they are the only two candidates in rows 1 and 5, these two numbers cannot appear anywhere else in the row, thus you can remove them.
In the example, the two candidate pairs circled in red, are the sole candidates. Since 4 and 7 must be placed in either of these two cells, all of the pairs circled in blue, can remove those numbers as candidates. In this puzzle, this means 1 becomes sole candidate in the second row; 2 becomes sole candidate in row 6; and thus, 6 is sole candidate for row number 4.
You can also use this technique if you have more than two candidates. For example, let us say the pairs circled in red were instead triple candidates of the numbers 1, 4, 7. This would mean those three numbers would have to be placed in either rows 1, 2 or 5. We could remove these three numbers as candidates in any of the remaining cells in the column. Hidden subset This is similar to Naked subset, but it affects the cells holding the candidates.
In this example, we see that the numbers 5, 6, 7 can only be placed in cells 5 or 6 in the first column marked in a red circle , and that the number 5 can only be inserted in cell number 8 marked in a blue circle.
Since 6 and 7 must be placed in one of the cells with a red circle, it follows that the number 5 has to be placed in cell number 8, and thus we can remove any other candidates from the 8th cell; in this case, 2 and 3. Sudoku pencilmarking is a systematic process writing small numbers inside the squares to denote which ones may fit in. After pencilmarking the puzzle, the solver must analyze the results, identify special number combinations and deduce which numbers should be placed where.
Here are some ways of using analyzing techniques:. In this example, squares c7 and c8 in box 7 can only contain 4 and 9 as shown with the red pencilmarks below. In addition, square a6 excludes 6 from being in the left column of box 7. As a result the 6 can only be in square b9. Such cases where the same pair can only be placed in two boxes is called Disjoint Subsets, and if the Disjoint Subsets are easy to see then they are called Naked Pairs.
The previous solving technique is useful for deducing a number within a row or column instead of a box. In this example we see that squares d9 and f9 in box 8 can only contain 2 and 7. The numbers which remain to be placed in row 9 are 1, 6 and 8. Disjoint Subsets are not always obvious to see at first sight, in which case they are called Hidden Pairs. If we take a very close look at the pencilmarks in row 7 we can see that both 1 and 4 can only be in square f7 and square g7.
This means that 1 and 4 are a Hidden Pair, and that square f7 and square g7 cannot contain any other number. Using the scanning technique we see that 7 can only be in square d7.
The X-Wing technique is used in rare situations which occur in some extremely difficult puzzles. Scanning column a we see that 4 can only be in square a2 or square a9. Similarly, 4 can only be in square i2 or square i9. Because of the X-Wing pattern where boxes are in the same row or column , a new logic constraint occurs: it is obvious that in row 2 the 4 can only be either in square a2 or in square i2, and it cannot be in any other square.
Therefore 4 is excluded from square c2, and square c2 must be 2. My profile My account. Log in. Become a member. Play new puzzles each week.
0コメント