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. Advanced solving techniques As seen on Times Online in February 2007

Sudoku solver