For more difficult puzzles see my collection of printable free sudoku puzzles. As we saw in the previous chapter, alternation is just what X-Cycles are about. But it turns out they are all part of a larger extended family. You will be able to solve the puzzle quickly now.Ĭongratulations on solving a very difficult Sudoku puzzle. It's very useful to split out chain-like strategies into X-Wings, XY-Chains, Forcing Chains, XYZ-Wings, X-Cycles, Nice Loops and so on, since they have special characteristics which make them spottable. Solve the naked single and the logjam is broken. When you remove the 4s, you now expose a naked single in (R7, C7). The cells circled in red may have the number 4 removed from them safely. Therefore, it is safe to eliminate the 4s from column 3 and column 7 except for the highlighted positions. We do know that it must reside in two of the four positions highlighted. At this point, we do not know which pair the 4 will reside in. Sudoku rules forbid any other combination. This means the 4 will reside in the pair (R2,C3) and (R5,C7) or in the pair (R2,C7) and (R5,C3). The two positions have to be diagonally opposites forming an X (hence the name). The number 4 can only appear in two of the four positions. These four positions are highlighted in grey. In row 5, the cells are (R5, C3) and (R5, C7). In row 2, the cells are (R2, C3) and (R2, C7). You shouldnt pay attention to the 3x3 blocks as. Each row has the number 4 in only two cells. wing is an advanced sudoku technique, which is based on the two parallel rows or two parallel columns. Observe that every three-by-three region, row, and column contains every number from 1-9 exactly once. Comparing the above puzzle to the one below will help you understand the differences. In the example shown, an X Wing pattern occurs in row 2 and row 5. In sudoku, the goal is straightforward: Fill in any row, column, or 3×3 region with the numbers 1-9 exactly once. This candidate must reside in both rows and share the same two columns or vice versa. The XY wing or Y wing technique The XY wing technique is a technique that is often compared to the hooks of an eagle and its prey. If these terms are not familiar, read my article Sudoku Tips for an illustrative guide.Īn X-Wing pattern occurs when two rows (or two columns) each contain only two cells that hold a matching candidate. The swordfish technique follows the same principle as the x wing, with the twist of having three basic sets rather than two. You will need to solve naked singles, hidden singles, a naked pair (4,7) in row 7, a locked candidate (5) in column 7, and a naked triple (2,4,5) in column 1 first. If you have trouble getting to this position, follow the steps I have outlined in my article “How to Solve Sudoku” X-Wing”. You will need to partially solve the puzzle to reach the picture shown.
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