Not to say that it might have been discovered elsewhere, I can't check, but please come forward if there are earlier references. In the red example, swapping within the box does not change the content of that box.Īs of January 2021 we have a new Unique Rectangle elimination! Thanks to Ivar Ag�y from Norway who shared an example with me. Why? Swapping the 7 and 9 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 9 in an alternate manner will produce two valid Sudokus. The 7/9 still resides on two rows and two columns, but instead of two boxes it is spread over four boxes. The pattern ringed in green 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 5 in that cell and the others would be the reverse. If the cell solution was 4 then we quickly know what the other three cells are. Such a group of four pairs is impossible in a Sudoku with one solution. They reside on two rows, two columns and two boxes. The pattern in red marked A consists of four conjugate pairs of 4/5. In Figure 1 we have two example rectangles formed by four cells each.
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