Sudoku Algorithms

The Bivalue Universal Grave (BUG) is a Sudoku-solving technique based on the assumption that a Sudoku puzzle, where all remaining cells contain just two candidates, does not have a unique solution. The image on the left shows a real-life example of this situation. The only cell that has three candidates is E7. Each candidate appears twice in each row, column, and square, except for the number '4' marked green, which appears three times in row E, three times in column 7, and three times in the last square of the middle row. If we remove hint 4 from this cell, we will have a “Deadly Pattern.” The only way to prevent this is to assign the value 4 to cell E7.

The image on the left presents another example of the Bivalue Universal Grave (BUG) technique. All cells in this puzzle have two candidates except for cell H8, which has three candidates. Additionally, each candidate appears twice in each row, column, and square, except for the number '1' marked green, which appears three times in row H, column 8, and the last square. If we remove the number 1 from cell H8, it will appear twice in each row, column, and square, and the puzzle will not have a unique solution. To maintain a unique solution, we need to assign the number 1 to cell H8.