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### Interaction, or Block and Column/Row Interaction, or Box/Row Claim, or Intersection, or Locked Candidates - Advanced Solving Sudoku Technique

Interaction by createclassicsudoku.com

a.k.a. Box/Row Claim by humage.com

Interaction, or Locked Candidate, or Interesection, or Box/Row Claim:

If in a 3×3 box all candidates of a certain digit are confined to a row or column, that digit cannot appear outside of that block in that row or column. That being said, that row or column outside of the block can remove this digit from their candidate values.

or

If in a row (or column) all candidates of a certain digit are confined to one 3×3 box, that candidate that be eliminated from all other squares in that 3×3 box.

Candidate Numbers (or Candidate Values) of an blank/empty square is a list of 'possible values' or candidates for this blank/empty cell.

In the ninth 3×3 box all candidates of number 2 are confined to the seventh row.

Remove number 2 from R9C9.

Above is an example of using InteractionRowBox(a.k.a. Intersection, Locked Candidates, or Row Claim) to refine the candidate values of R9C9 (the highlighted squares in the ninth 3×3 box excluding the seventh row). Blank/Empty Squares are marked with candidate values in red.

In the ninth 3×3 box all candidates of number 2 are confined to the seventh row, therefore number 2 cannot appear outside of the ninth box in the seventh row. That being said, R8C8 and R9C9 can remove this digit from their candidate values. Note that only R9C9 contains number 2 as a candidate value, so we can remove number 2 from R9C9's candidate values.

the seventh row all candidates of number 8 are confined to the eighth 3×3 box.

Remove number 8 from R7C7 and R7C9's candidate values.

Above is another example of using Interaction(a.k.a. Intersection, Locked Candidates, or Box Claim) to refine the candidate values of R7C7 and R7C9 (the highlighted squares in the seventh row excluding the eighth 3×3 box). Blank/Empty Squares are marked with candidate values in red.

In the seventh row all candidates of number 8 are confined to the eighth 3×3 box, therefore number 8 cannot appear outside of the seventh row in the eighth box. That being said, R7C7 and R7C9 can remove number 8 from their candidate values.

For convenience, in our Sudoku solver, we call

InteractionBoxRow:

If in a 3×3 box all candidates of a certain digit are confined to a row, that digit cannot appear outside of that box in that row. That being said, that row outside of the block can remove this digit from their candidate values.

InteractionBoxCol:

If in a 3×3 box all candidates of a certain digit are confined to a column, that digit cannot appear outside of that box in that row or column. That being said, that column outside of the block can remove this digit from their candidate values.

InteractionRowBox:

If in a row all candidates of a certain digit are confined to one 3×3 box, that candidate that be eliminated from all other squares in that 3×3 box.

InteractionColBox:

If in a column all candidates of a certain digit are confined to one 3×3 box, that candidate that be eliminated from all other squares in that 3×3 box.

### How to find them?

• Use basic methods to solve the Sudoku until no further blank/empty square can be inferred to be a number using basic methods (Sole Candidate and Hidden Single).
• Write down the candidate values for every blank/empty square.
• Check whether in a 3×3 box all candidates of a certain digit are confined to a row or column, that digit cannot appear outside of that block in that row or column. If there exist such a digit, remove this digit from candidate values of blank squares in that row or column but not in this box.
• Check whether in a row (or column) all candidates of a certain digit are confined to one 3×3 box, If there exist such a digit, remove this digit from candidate values of blank squares in that box but not in the row or column.

##### Solving Sudoku Methods Explained

This article answers questions: What are commonly used solving sudoku methods? What solving Sudoku methods do we use? In what sequences?

##### Basic Solving Sudoku Method: One Choice

a.k.a Sole Candidate, Only Candidate, or Naked Single

##### Basic Solving Sudoku Method: Elimination

a.k.a Hidden Single, Loner

##### Advanced Solving Sudoku Method: Subset2

a.k.a Pair, Naked Pair, or Naked Twins

##### Advanced Solving Sudoku Method: SubsetPosition2

a.k.a Hidden Pair or Hidden Twins

Last updated 3 mins ago

##### Advanced Solving Sudoku Method: Interaction

a.k.a Box/Row Claim or Intersection , or Locked Candidates

##### Solving Sudoku Methods Explained

This article answers questions: What are commonly used solving sudoku methods? What solving Sudoku methods do we use? In what sequences?