![]() So all conditions are met - 3 rows, 3 columns. The cells containing the six entries are lined up exactly in 3 columns (1, 2, and 9 - for clarity, they are also highlighted with a white and orange border). There are only 2 occurrences of the six in each of these rows. Wikipedia Backtracking: Detailed explanation of the backtracking algorithm, its applications, and examples. In the example, the "fish digit" is a 6, and the lines 1, 6, and 9 are the "base" (highlighted by the green guide lines). Wikipedia Sudoku: In-depth history and explanation of Sudoku puzzles, including variations and solving techniques. First, we need to find the so-called "fish digit" and the "base". Let's look at an example of using the Swordfish technique. That is, to use the technique, you must go to a certain level of abstraction and find three rows or three columns that each have two occurrences of candidate numbers. In mechanics, "Swordfish" is similar to "X-Wing", but uses 3 columns and 3 rows instead of two. The technique helps to exclude hypothetically suitable candidate numbers and to reduce the scatter in the selection. I leave the rest of the solution to the readers.Ī second sudoku article can be found here.The "Swordfish" technique is used to solve hard Sudoku with many empty (unfilled) cells. The rest of the puzzle can be easily solved by basic techniques. After all the redundant candidates in the empty cells are removed by the technique of "naked pair" new single candidates begin to appear in the puzzle. This means the redundant option 3 can be removed from cells (1,7) and (2,7) forming a naked pair with the candidate numbers 4 and 8.Ī puzzle consisting of only single candidates and naked pairs should be classified under the easy category. As a result, the cells (9,7) and (8,8) form a new naked pair with the candidate numbers 5 and 6.įinally, the three cells (1,8), (2,8) and (3,9) in box 3 form a naked triplet with the candidate numbers 1, 3 and 9. ![]() Similarly, the redundant options 3 and 9 can be removed from cell (8,8). Hence the redundant options 2 and 3 can be removed from cell (9,7). The three cells (7,7), (7,9) and (9,9) in box 9 form another naked triplet with the candidate numbers 2, 3 and 9. ![]() Taking notes is mandatory if you’re solving complex puzzles. Note potential candidates in open squares. This may seem obvious to you, but some folks don’t do this It’s possible for adept players to solve. With more difficult Sudoku puzzles, you will reach a point at which Direct Solves no longer exist. How to Solve Hard Sudoku Puzzles Use a pencil. In fact, all easy-level puzzles can be completed using only Direct Solves. The best way to learn how to solve sudoku is to practice. What follows will provide you with some schemes to solve the complete sudoku. There will come a point when you will need to change your strategy. Continue to solve the more obvious numbers. This means that the three cells (6,2), (6,6) and (6,8) in row 6 form a naked triplet with the candidate numbers 5, 7 and 8. The best way to work through a Sudoku puzzle is to tackle the Direct Solves first, since they are the easiest. Look at box 8 and see where the number 7 should go. See the paragraph above Figure 4 if you cannot see why the 2 in (6,2) cannot be used. In row 6, the only position possible for a 2 is (6, 4).
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