![]() 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. For an outside square, the solution is always the outside total – 45.Advanced solving techniques As seen on Times Online in February 2007 In general, to use the 45 rule, look for a row, column or block where all cages except one lie completely inside.įor an inside square, the solution is always 45 – the inside total. In the case, it was easier to calculate the inside total, but if the cage lying partly outside has one square outside and more than one square inside, the outside total should be used to calculate the outside square. This could also have been solved another way, by finding the 'outside' total - the total of all cages within the column, including the one lying partly outside.Īgain, as all the squares within the column must add up to 45, the 'outside' square is 54 – 45 = 9. The 14 cage can now be completed by solving the other square as a 9. Now, as the whole column must add up to 45, the ninth square (the 'inside' square in this case as it is inside the column) must be 45 – 40 = 5. The numbers in this column will add up to 45.Īdditionally, because the first four cages in this column (the 15 cage, the two 9 cages and the 7 cage) lie completely within the column, the numbers in the first eight squares total 15 + 9 + 9 + 7 = 40.Ĭall this the 'inside total', because it is the total of all cages which lie completely inside the column. Take the first column of the Killer Sudoku shown in Figure 1. ![]() Therefore, the total of all numbers in one row, column or block will always be 45. This uses the fact that every row, column and block must contain each of the numbers 1 to 9 once. The 45 RuleĪn essential Killer Sudoku solving technique is the "45 rule". You will need new specialised Killer Sudoku solving techniques to progress in these puzzles besides the standard Sudoku techniques you will already know. Killer Sudoku adds a new dimension to standard Sudoku, requiring arithmetic to solve.
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