This means one of the corners could become a deadly pattern if certain candidates were removed. In example A, swapping within the box does not change the content of that box.įor all Unique Rectangles we are going to look for potential deadly patterns and take advantage of them. Why? Swapping the 7 and 8 around places them in different boxes and 1 to 9 must exist in each box only once. One of them is the real solution, the other a mess. Now, such a situation is fine since you can't guarantee that swapping the 7 and 8 in an alternate manner will produce two valid Sudokus. The 7/8 still resides on two rows and two columns, but instead if two boxes it is spread over four boxes. The pattern marked B looks like a deadly pattern but there is a crucial difference. If you have achieved this state in your solution something has gone wrong. There are two solutions to any Sudoku with this deadly pattern. But it would be equally possible to have 3 in that cell and the others would be the reverse. If the cell solution was 2 then we quickly know what the other three cells are. Such a group of four pairs is impossible in a Sudoku with one solution. The set with 2/3’s in box A is spread over two rows, two columns and two boxes Both contain four sets of pairs or bi-value cells. There is a crucial difference between both of them one of these is a “Deadly Pattern” and the other is a valid spread of candidates. In this diagram we have two rectangles formed from four cells apiece. If that proviso is admitted then pure logic let’s us do some fancy footwork. The following three strategies – Unique Rectangles, Empty Rectangles and the wonderfully named Bi-value Universal Grave (BUG) all rely on unique solutions to work. If it doesn’t lead to an error it will more often that not lead to non-uniqueness.

It’s easy to create a sudoku with more than one solution simply by missing of a clue or changing one.

This is very much the norm with all published Sudokus since no puzzle compiler would want to annoy their audience with puzzles that have two or more solutions. There is a family of strategies which rely on Sudoku puzzles having one single solution.

Techniques in solving sudoku puzzle