3 is a partially solved Sudoku, using easy and medium difficulty solving techniques no more squares can be solved using them. In this case, this particular number can be eliminated as a possibility for all other squares in those three columns.įig. This resembles the wings of a biplane, separated by struts.Ī swordfish is found when for three rows, there are two or three possible squares in which a particular number can be placed, and for all three rows these squares lie in the same three columns. If lines are drawn along the rows and columns, connecting the squares involved, they can form two rectangles, connected at the corners. The swordfish technique is named after a World War II biplane called the “Fairey Swordfish”, a Torpedo Spotter Reconnaissance biplane used by the Royal Navy from 1936 to 1945. The swordfish is similar to the x-wing technique, but on a larger scale, with three rows and columns instead of two. This is a more difficult method, one of the most complicated for any Sudoku you will find in print. From today onwards, you will find the swordfish technique become a regular feature in the Times2. Of course, you can exchange rows and columns in this definition. In this case, this particular number can be eliminated as a possibility for all other squares in those two columns. In general, an x-wing is found when for two rows, there are two, and only two, possible squares in which a particular number can be placed, and for both rows these squares lie in the same two columns. Now this square is solved, you can complete the Sudoku using easy methods. This leaves one square in the first column with only one pencil mark, so you can now place the 9. Using the same logic in the last column, you can also eliminate the 7 as a possibility from all squares which are not in either highlighted row (Fig. Now you can cross out the 7 pencil mark from all other squares in the first column. So, there are two possible ways of placing the 7 how does this help you solve anything? Well, you have established that the 7 for the first column must be in one of the two highlighted rows not in any other squares in this column. Therefore, they must be placed in diagonally opposite corners: one 7 in the first column one 7 in the last.

Neither can you place them both in the last column. It is a fact that you cannot place the 7 in the first column square of both the highlighted rows at the same time. Here, the only squares with the 7 as a possibility are in the first and last columns. You know it must be placed once, and only once, on each of these rows. In the diagram there are complete pencil marks for all squares in rows three and seven, and a necessary column/block intersection to eliminate a 7 pencil mark.Ĭonsider where you might place the 7 on the third and seventh rows (highlighted). Now, no more squares can be solved with these techniques you are stuck. 1 is partially solved using easy and medium difficulty solving techniques: singles, hidden singles and column/block intersections. The term x-wing itself derives from the x-wing fighters in Star Wars. There is a relationship between the diagonally opposite squares, hence the “x” in x-wing. The x-wing techniqueĮssentially, this method uses the fact that in certain cases, there are only two possible ways of placing two numbers in four squares which form a rectangle. Whenever you solve a square, you must remove that number from the pencil marks in all other squares in the same row, column and block. With many advanced techniques, the key is to spot patterns within your pencil marks to eliminate possibilities within other squares. Pencil marks are small numbers, usually written at the top of each unsolved square, listing all the possible values for that square. Here we present the techniques that will help you solve the hardest puzzles using only logic and no guesswork.įirst a couple of preliminary points: if you have ever completed any Fiendish or Super Fiendish Sudoku, you will be familiar with noting down candidates or pencil marks. Please be reassured that all Sudoku puzzles published in the Times are always solvable by logical means. So, as we increase the difficulty Super Fiendish, the time has come to present the essential techniques for solving the most difficult Sudoku puzzles. Many have welcomed the new challenge but some have asked for help. In November 2006, The Times introduced a new extreme level of Sudoku giving players a more difficult level of logic: Super Fiendish. This will help you to quickly note all possibilities for any given cage when solving a Killer Sudoku puzzle.Advanced solving techniques As seen on Times Online in February 2007 Below are all possible combinations of numbers that can be placed in a Killer Sudoku cage, given the cage size and the cage total.

Solving sudoku step by step