Menu
Skip Navigation Links.

Sudoku Algorithms

Rectangle Elimination
The picture below illustrates the Rectangle Elimination Sudoku solving pattern. This pattern involves cells in two rows and two columns; in our example, rows A and F, and columns 1 and 6. There are only two candidates for the number 6 in column 5. If one candidate is removed, the other must be assigned to its cell. This relationship, known as a strong link, is crucial in the Rectangle Elimination pattern.
Rectangle Elimination Example If candidate 6 is assigned to cell F1, candidate 6 should be removed from cell F5, and the value 6 will be assigned to cell A5 due to the strong link. Having the number 6 in cells F1 and A5, along with any candidate 6 in the top left square, will violate Sudoku rules. Therefore, assigning the value '6' to cell F1 will result in an invalid puzzle, and the candidate should be removed
Rectangle Elimination Example The picture on the left illustrates another example of the Rectangle Elimination technique. The pattern is formed by candidate 4 in rows C and F and columns 3 and 5. If cell F5 has a value of 4, then candidate 4 in cell F3 should be removed. There is a strong link between the two candidate 4 in column 3. When 4 is removed from cell F3, this value should be assigned to cell C3. Therefore, if we have a value of 4 in cells F5 and C3, all other candidate 4s should be removed from rows C and F and columns 3 and 5. In this case, the value 4 does not exist in the top middle square, rendering the sudoku puzzle invalid. Our assumption that cell F5 has a value of 4 is incorrect, and we can remove candidate '4' marked red from this cell.