Xyz wing sudoku strategy9/9/2023 Searching for missing numbers in rows and columns: So the only square left for 1 in box 2 is square d2. Whichever the case may be, the 1 of column e is in box 8 and it is therefore not possible to have 1 in the centre column of box 2. In this example the 1 in square c8 implies that either square e7 or square e9 must contain 1. There are more complex ways to find numbers by using the process of elimination. Eliminating numbers from rows, columns and boxes: Eliminating all the above numbers leaves 2 as the single candidate for square b4. Taking a careful look at square b4 we can see that 3, 4, 7 and 8 are already used in the same box, 1 and 6 are used in the same row, and 5 and 9 are used in the same column. Often only one number can be in a square because the remaining eight are already used in the relevant row, column and box. This means that square i3 is the only place left for 1. However, square g4 also contains 1, so no additional 1 is allowed in column g. In this example, row 1 and row 2 contain 1s, which leaves two empty squares in the bottom of box 3. The same technique can be expanded by using information from perpendicular rows and columns. This leaves square e1 as the only possible place into which 9 can fit in. Looking at box 1 and box 3 we can see there are already 9s in row 2 and in row 3, which excludes the two bottom rows of box 2 from having 9. In our first example we will focus on box 2, which like any other box in Sudoku must contain 9. Here are some ways of using scanning techniques: 1. The scanning technique is also very useful for hard puzzles up to the point where no further progress can be made and more advanced solving techniques are required. The scanning technique is fast and usually sufficient to solve easy puzzles all the way to the end. The easiest way starting a Sudoku puzzle is to scan rows and columns within each triple-box area, eliminating numbers or squares and finding situations where only a single number can fit into a single square. The grid is also divided into nine 3x3 sub-grids named boxes which are marked box 1 through box 9. My own personal experience is that it is not common to find that you need this technique to solve a puzzle.Sudoku grid consists of 81 squares divided into nine columns marked a through i, and nine rows marked 1 through 9. Net result: any "5" along a red line that's not in a blue line can be removed (all the 5s in the pink cells can be erased).Īpparently, some examples of this technique create a pattern that resembles the actual fish it's named after. We don't know which blue line we just know it's at a blue line. The result is each red line's 5 is going to be where a blue line crosses it. Why is this important? Well, it isn't - unless the red lines have other 5s in them somewhere! You see, each of the three blue rows is going to have a 5, and since the possible locations are limited, each row will end up having a 5 in one of the red lines. Let me say that a different way: The blue lines only have 5s where the red lines cross. Here is the same puzzle, but with some markings added for illustration:Īs you can see, the three rows marked by the blue lines all have their possible locations for a 5 confined to the same three columns (marked by the red lines). There are three rows where all the possible 5s appear in the same three columns. The puzzle above has a Swordfish on the number 5. It is not super complex to understand - it's just very hard to spot one.īut, in the interest of being complete, I will cover it. I must confess - this is probably my least favorite technique. Even if you know it's there, it can take some time to find. Just as the X-Wing involves two candidates in two columns or rows, the Swordfish involves three candidates in three columns or rows.
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