Subset2, or Pair, or Naked Twins, or Naked Pairs - Advanced Solving Sudoku Technique
Subset2 by createclassicsudoku.com
Pair by Mensa Guide to Solving Sudoku
Naked Twins by humage.com
Naked Pair by hodoku
Subset2, or Pair, or Naked Pair, or Naked Twins:
If two blank squares in a same row/column/box has same two candidate numbers, then other empty squares in this row/column/box can remove these two numbers from their candidate numbers.
Candidate Numbers (or Candidate Values) of an blank/empty square is a list of 'possible values' or candidates for this blank/empty cell.
Below is an example of using Subset2(a.k.a. Pair, or Naked Pair, or Naked Twins) to refine the candidate values of R7C1, R7C6, and R7C7. Blank/Empty Squares are marked with candidate values in red.
Solve medium Sudoku on 03/13/2018 in a step-by-step style
For the seventh row, R7C3 and R7C4 have same two candidate values {1, 4}. Therefore, it is safe to remove numbers 1 and 4 from the candidate numbers from other blank/empty squares in the seventh row. After we remove numbers 1 and 4 from R7C7's candidate values, R7C7 has one and only one candidate value (number 8) left. Therefore, R7C7 must be filled with number 8.
For convenience, our Sudoku solver names 3 different categories of Subset2.
Subset2Row:
an untaken number in a row only show up in one empty square as its candidate values, then this empty square must take the number.
Subset2Col:
an untaken number in a column only show up in one empty square as its candidate values, then this empty square must take the number.
Subset2Box:
an untaken number in a 3×3 box only show up in one empty square as its candidate values, then this empty square must take the number.
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 every row/column/box to see if there are two blank/empty squares have same two candidate values.
- When there are two blank/empty squares with the same two candidate values, remove these two values from other blank/empty squares in the same row/column/box.