Unique Rectangle Type 1Īny Sudoku puzzle must have only one possible solution. However, the cell at the intersection of both branches of the Y contains a shared digit by both (number 1), allowing the player to eliminate it as a candidate to that cell. If any of the cells on the red paths contained one candidate shared by the cells on the extremities of the lines, it could be eliminated, but this is not the case. In the example above, the stem cell contains the digits 2 and 9 (highlighted in orange) and connects to the branches, each with one of these digits as candidates (purple squares). If any of the shared digits are candidates within the lines connecting the cells or at an intersection point, they can be safely removed. The next step is to trace lines in each row and column of the cells to form a square or rectangle. With a bit of mental effort, the player can picture a Y when connecting them, with one cell working as the stem and the remaining as the branches. The XY-Wing is a strategy to remove candidates. It can be applied when there are three cells in the grid, each with only a pair of candidates that share at least one digit among them (e.g. Out of the advanced Sudoku strategies, the forcing chains method is usually a last resort as the chains can be very long and complicated and they do not always produce results.

5 is still the answer to the highlighted cell. The chain would be longer, but the result is the same.

Note that when testing for number 1, the player could also have made a chain by going right (to the cell with 1 and 4 as candidates). Therefore, this digit will be the solution for that particular cell. When testing for both digits, the player finds that the outcome for the highlighted cell with candidates 5 and 7 is always 5. In this example, the top highlighted cell with the candidates 1 and 2 was used to apply the forcing chains technique. If so, that will safely be the solution for it. The goal is to find if there is a cell that would bear the same result whichever digit is used. The player picks one and begins testing the changes to puzzle when applying each of the two digits in that cell. To apply a simple forcing chain, there must be cells with only two candidates in the grid. When it does work, it gives the player the solution for one cell. Unfortunately, applying it requires very high levels of concentration and the outcome can be uncertain. Forcing Chainsįorcing chains is one of the easiest advanced Sudoku strategies to understand. It can then be safely removed from that cell, leaving only numbers 1 and 2 as candidates to it. When testing them on the grid, the player finds that the 4 highlighted in red would be an impossible candidate in both cases. Thus, there are only two sets of possibilities within this chain for number 4, the green and the yellow sets. In this grid, number 4 is a candidate to two cells in three different rows, allowing the player to use the Swordfish technique.Ĭonnecting them reveals that whenever a digit highlighted in green is possible, the yellows become impossible and vice-versa. The player can then put them to the test and eliminate that number as a candidate to the cells where it would become impossible in both cases. These cells must also be united by column, regardless of the shape they create.Ĭonnecting them will result in a closed chain that reveals two sets of possible placements for that digit. To apply it, the player must find a digit candidate to two cells in the same row, in three different rows. This strategy helps to eliminate a candidate from cells too. It can then be eliminated as a candidate to that cell.

Testing the pairs on the grid shows that the 5 highlighted in red would be impossible in both cases. By connecting the cells containing it, it is easy to see that in this situation only the pairs in green or yellow could be possible. In this example, the number 5 forms the necessary pattern to apply the X-Wing strategy. The next step will be to test those sets on the grid and eliminate the digit from any cell that would become impossible in both situations. By making an X linking diagonally the two opposite extremities of this rectangle, the player finds only two possible sets of positions for that digit. The player can use this strategy when there is one candidate repeated in four cells that form a square or rectangle when mentally connected by row and column. It can also be applied in some intermediate levels, although its incidence is very low in these cases. The X-Wing method is one of the most basic advanced Sudoku strategies. Regardless, their application always demands high levels of concentration from the player as they work by deduction. Advanced Sudoku strategies are used in the hardest levels of these puzzles and they can either help to reduce candidates or to find the solution for a specific cell.

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