Sudoku of the Day | Sudoku Techniques
Guide to solving sudoku puzzles. This page covers techniques that will solve most puzzles up to (and the lines from rows and columns outside the square criss-cross each other. . The remaining three rules let you remove numbers from candidate lists, reducing them down towards meeting one of the first two rules. Below are the most common techniques you can use once you've covered the you with a direct placement, but help you by allowing you to cross out one or. Are there Sudoku puzzles that are faster to solve by guessing? If you do a web search for Sudoku solving techniques, you will find that there.
If A turns out to be a 7 then it rules out a 7 at C as well as B. If this is the case then any other 7s along the edge of our rectangle are redundant. We can remove the 7s marked in the green squares.Lesson 7. The cross /meet technique.
The rule is only two possible cells for a value in each of two different rows, and these candidates lie also in the same columns, then all other candidates for this value in the columns can be eliminated. The reverse is also true for 2 columns with 2 common rows. Since this strategy works in the other direction as well, we will look at an example next.
From the Start In this second example I've chosen a Sudoku puzzle where an enormous number of candidates can be removed using two X-Wings. The first is a '2-Wing'. The yellow high lighted cells show the X-Wing formation.
Note that the orientation is in the columns this time, as opposed to rows as above. Looking at columns we can see that candidate 2 only occurs twice - in the yellow cells. X-Wing example 3 A few steps later the second X-Wing is found on candidate 3 in the same rows. Generalising X-Wing X-Wing is not restricted to rows and columns.
We can also extend the idea to boxes as well. If we generalise the rule above we get: One is known as a "naked pair. For example, 1 and 9. Since there are two cells and only two digits the same twothen one of the digits must belong to one of the cells and the other digit must belong to the other cell.
But even before you determine which cell takes the 1 and which one takes the 9, you already know that the 1 and 9 cannot go anywhere else in that region.
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So if these twin cells are in the same block, then the 1 and the 9 cannot go in any other cell within that block. If the twin cells are in the same row, then the 1 and 9 cannot go in any other cell within that row; the same is true if the twin cells are in the same column. If you have pencilled in any candidates, then you can use this principle of twinning to eliminate the twin digits from other cells in the same region, if they have shown up elsewhere.
Or you can avoid placing them in there in the first place, as you notice in the picture here. In that case, placing the candidates in Block 9 shows that only the 5 and 9 can be used in the empty cells.
Since they are both in the same row, then neither 5 nor 9 can appear as a candidate in any other cell within that row. If you first filled in the candidates for Row 8 of Block 8, you could include the 9 in cells 84 and 86 - initially. But then, upon completing Block 9 or completing Row 9 of Block 8, you would see a Twin Pair a Naked Pair containing a 9; that tells you that the 9 could not be used either in cell 84 or The second way that twinning works a "Hidden Pair" - not shown here happens in a situation when other digits occur in the same cells as the twin digits - but those two digits appear only in two cells in that region row, column, or block.
In that case, all the other digits can be eliminated from those two cells. As an example, let's say that the candidates in cell 57 are 1, 4, 6, 7, and 8, and the candidates in cell 59 are 1, 2, 5, 8, and 9.
You see that 1 and 8 appear in both of these cells, which are in row 5. As you check across that row, you see that no other cells offer 1 or 8 as a candidate.
In other words, even though other candidates appear to be possible in cells 57 and 59, the 1 and the 8 have no other possible homes in row 5. Therefore, you can eliminate all other digits as candidates for those two cells.
When you do that, even though you still may not know where the 1 and the 8 go, you will eliminate theoretical placement for those other digits, and that may lead to certainty of where to place them. Triplets and beyond work in the same two ways, but with a slight variation.
In those cases, it is not necessary that all three digits appear in all three cells. For example, let's say you see a row that contains a cell with 6 and 7 as the only candidates; two other cells in the same row contain only 6, 7, and 8. That makes up a triplet. The 6, 7, and 8 must go in those three cells but the 8 cannot go in the first one mentioned.
Sudoku X-Wing Identification And Solution
That also tells you that those three digits cannot be used in any other cells in that row. But it could also be true that one of the cells contains only 6 and 7; a second one in the same row contains only 7 and 8; and a third one still in the same row contains only 6 and 8.
That is also a triplet. Those three digits must be used in that row only in those three cells, but limited as indicated. In this situation, you have completed all the cells that you can determine with certainty; then you have pencilled in the candidates in the remaining cells, keeping aware of Twinning, etc.
You want to pencil in all candidates, but only the ones that are truly possible. After using the pencilled-in candidates to solve additional entries with certainty, you can use the Forced Choice technique. With this, you choose one cell which contains only two candidates, and you select one of them as your "choice. I mark this cell with an asterisk, so that I can remember where I started.
Since you don't know yet whether that choice is correct, use some method of "choosing" that will alert you to the choice without erasing the other candidate. You may decide to underline your Choice, draw a circle around it, or lightly pencil-slash through the unselected one, for example. When you have chosen one of the candidates, check other cells in the same row, column, and block, to see which candidates are forced because of the choice you made, and then mark them similarly.
Remember that you don't know yet whether these choices are correct; you are essentially following a hypothesis to its inevitable conclusion.
Techniques For Solving Sudoku
You will either come to some point where a choice contradicts another one by selecting a candidate that had previously been selected in another cell in the same regionor you might solve the entire puzzle. A third, unpleasant, possibility is that the puzzle is so complex that you can neither solve it nor find a contradiction. In that case, you will need even more advanced techniques. It would be so nice if a long string of non-contradictions proved that you were on the right track, but that is not always true.
There have also been some times when the Forced Choice was so difficult that I realized it's time for me to look into the next level of solving techniques. When I do that, I will come back and share them with you! Forced Choice works best when you find a good cell as your starting point.