![]() ![]() This is because the alignment between A3 and B9 means they both see six common cells. This example starting with the hinge at A8 removes four 8’s from the first two rows. Either way the far corner at G1 can’t be a 4. ![]() Here is a classic Y-Wing beginning with the hinge at C4. BC and AC can see all the cells marked with a C where elimination can occur. A is a locked pair because they share the same row. In the example shown, a Sudoku Swordfish pattern occurs in rows. This candidate must reside in each of the three rows and share the same three columns or vice versa. A Swordfish pattern occurs when three rows (or three columns) each contain 2 or 3 cells that hold a matching locked candidate. In Figure 2 B is a locked pair because they share the same box. Sudoku Swordfish is a variation of the X-Wing pattern. If our A, B and C are aligned more closely they can 'see' a great deal more cells than just the corner of the rectangle they make. It’s impossible for a C to live there and if C resides there it can be evicted. The cell marked with a cross can be 'seen' by both Cs - the cell is a confluence of both BC and AC. So whatever happens, C is certain in one of those two cells marked AC or BC. AC/BC is a complimentary pair, meaning they will both be either true or false. If AB turns out to be B then C is certain to occur in the top right. If the solution to that cell turns out to be A then C will definitely occur in the lower left corner. It requires the use of pencil marks and cross referencing several cells. Lets see which cells can contain the digit 8 in those two rows, they are highlighted in red. C is the common candidate between AC and BC. Take a look at row number 2 and row number 4 in this puzzle. The bottom left cell marked AC is also bi-value and so is BC. XY Wing The XY Wing strategy uses three cells that contain two and only two candidates and have common values in the cells. B also only exists twice in its row.ĪB is a bi-value cell (it only has two candidates). Note how the 3 cells form a 'Y' (see the red lines - it's really more like a 'V'). These cells (called pincers) should be in the. Then, we'll look for two more cells with 2 notes as well. To start, we need to find a cell with exactly two notes. Let's take a look at this technique with an example. That is the candidate number represented by A only exists twice in the column. XY Wing involves 3 different cells each with exactly two candidates (pencil marks) that are related to each other in such a way that you can make some logical conclusions. 'Y-Wing' technique is similar to 'X-Wing', but it based on three corners instead of four. Let’s look at Figure 19.1 for the theory.Ī is a conjugate pair and so is B. The forth corner is where the candidate can be removed but it leads us to much more as we'll see in a minute. It starts by finding a cell with only two candidates (a bi-value cell) called the pivot. The name derives from the fact that it looks like an X-Wing - but with three corners, not four. XY Wing (aka Y Wing) XY Wing (sometimes called Y Wing) is another advanced technique for eliminating candidates. This means that any cell that is seen by both r3c3 and r8c5 cannot contain the digit 5, so we eliminate 5 from r3c5.This is an excellent candidate eliminator (and is also known as XY-Wing). Thus, this is a Double Implication Chain and we showed that either r3c3=5 or r8c5=5. Similarly, by reversing the direction, if r8c55, then r3c3=5. ![]() Now, if r3c35, then we have r3c3=1, which implies r7c3=1 and so r8c5=5. What does this XY-chain mean? Note that both ends of the chain involves the digit 5 as a candidate. The following example shows a XY-chain resulting in an elimination. Here, candidate 1 is forbidden from all the blue cells. The basic principle of this technique is simple. In this example we have moved things around a bit. These cells must be aligned by column and row, forming a square or rectangle when connected. To be able to apply this technique, the player must find 2 rows or 2 columns where a single digit is a candidate in only two cells of each. The shortest XY-Chain is an XY-Wing with only 3 cells.Ī XY-Chain is both a Double Implication Chain and a Alternating Inference Chain. Requirements to apply the Sudoku X-Wing strategy. ![]() A XY-Chain is a chain of cells which each contain only 2 candidates.īecause the chain is entirely made up by bivalue cells, the link between the 2 candidates in each cell cause strong inference, which allows us to use weak inference between the cells. ![]()
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