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. There are also two examples which show the pitfalls of Uniqueness strategies - and how they do not always apply in the case of Sudoku X.Advanced solving techniques As seen on Times Online in February 2007 Some of the basic strategies are illustrated after the examples and show how they can be extended to the diagonals. As the grade increases the diagonals contain much more important information. Gentle puzzles should require little to no note taking and can often be solved with normal ‘eye-balling’ techniques. This rule is in proportion to the difficulty.
But to complete tough and harder puzzles the solver must be expected to use the extra diagonals. In Sudoku X all the normal Sudoku strategies apply - and there are a great number of these. Note, it is perfectly possible to create a normal Sudoku that co-incidentally has the unique 1 to 9 in each diagonal but unless this information is revealed first it is usually of no help to the solver. However, these extra constraints allow the puzzle compiler to reduce the number of necessary clues thus creating a balanced puzzle that rivals normal Sudoku in variety and difficulty. The puzzle solver can use this information to reduce the possibilities in those lines and make deductions across the the board previously out of reach in a normal Sudoku. In Sudoku X the two diagonals containing nine cells and sharing the central grid cell must also be filled with exactly 1 to 9. There are nine ‘cells’ in every row, column and box. In a normal Sudoku puzzle all rows, columns and 3x3 boxes must be filled with the numbers 1 to 9 without repeating a number. This is a variant of the popular Sudoku puzzle which contains two extra constraints on the solution, namely the diagonals, typically indicated by grey cells.
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