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### Elimination, or Hidden Single, or Loner - Basic Solving Sudoku Technique

Elimination by Mensa Guide to Solving Sudoku
a.k.a. Hidden Single by hodoku
a.k.a. Loner by humage.com

Elimination, or Hidden Single, or Loner:
An untaken number in a row/column/box only show up in one empty square as its candidate values, then this empty square must take the number.

Below is an example of using Elimination(a.k.a. Hidden Single, or Loner) to fill R4C3 (the square in the fourth row and the third column).

For the fourth row,

• Number 6 cannot be in R4C4 (within its belonged 3×3 box, number 4 is already taken by R6C5);
• Number 6 cannot be in R4C8 or R4C9 (within its belonged 3×3 box, number 6 is already taken by R5C7);
• Therefore, number 6 has to be in R4C3. That being said, R4C3 is the only square where number 6 can be put in the fourth row.<

For convenience, we call

Row-Elimination:

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.

Column-Elimination:

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.

Box-Elimination:

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?

Scan numbers that have been taken by squares. For example, in the above example,

• Seven 7s, Six 9s, Five 6s, four 3s, three 2s, three 5s, three 8s, two 1s, two 4s. So we check numbers in the order of 7, 9, 6, 3, 2, 5, 8, 1, and 4.
• Check number 7. However, we cannot finalize 7 in the second row or the eighth row; and we cannot finalize 7 in the seventh and the nineth column; and we cannot finalize 7 in the third box and the ninth box.
• Check number 9. However, we cannot finalize 9 in the second row, or the third row, or the fifth row; and we cannot finalize 9 in the fourth column, or the sixth column, or the seventh column; and we cannot finalize 9 in the the second box, or the third box, or the fifth box.
• Check number 6. We can finalize that 6 in the fourth row. For the fourth row, the only place 6 can be put in is the third 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?