Group Bound

Description

The Group Bound algorithm helps you identify candidates which can be elliminated due to a restriction placed by one group onto another. For example the fact that a candidate can only be in two cells for a given row, which also are inside a region, means that the region can only have that candidate in those two cells.

Reasoning

When groups overlap, they can impose candidate restrictions on each other, if the candidate only appears in the overlaping cells.

Examples

Box Example

4 is a candidate only on row 1 in box 3.

That means that candidates 4 can be removed from all other cells on row 1 that are outside of box 3: cell [1,6].

Row Example

7 is a candidate on row 7 only in box 7.

That means that candidates 7 can be removed from all other cells in box 7 which are not in row 7, cells [8,3] and [9,3].

Column Example

1 is a candidate in column 6 only in box 8.

That means that candidates 1 can be removed from all other cells in box 8 which are not in column 6: cells [9,4] and [9,5].

Algorithm

  1. Fill in all the pencil marks in the puzzle.
  2. For every available digit 1 to 9
    1. For every region
      1. Check if the digit only occurs in 1 row.
      2. If yes, then we can remove all the candidates from that row that are outside of the region.
      3. Check if the digit only occurs in 1 column.
      4. If yes, then we can remove all the candidates from that column that are outside of the region.
    2. For every row
      1. Check if the digit only occurs in one region.
      2. If yes, then you can remove the digit candidate from that region which are not in the row.
    3. For every column
      1. Check if the digit only occurs in one region.
      2. If yes, then you can remove the digit candidate from that region which are not in the column.

Practice Puzzles

If you tap on the following links on an iOS device which has the Sudoku Tutor app installed, it will launch the app and open the practice puzzle. Tap hint once the puzzle is open to see the strategy in action.

Sample Puzzle 1
Sample Puzzle 2
Sample Puzzle 3

Next Step

Back to Sudoku Solvers or continue to next algorithm X-Wing