Eliminate Pairs, Triples and Quads

This is one of the simple solution methods which you will use regularly to solve the puzzle.
Example: after solving apart of the puzzle, you have gotten the following situation:

solve sudoku by finding equal pairs

In our example similar pairs appear in cells D6 and F6. Both cells contain the numbers (1,3). This means that if number 1 is the solution for cell H6 then number 3 will be the solution for cell F6 or the other way around.

Since each number can only appear once in every row, the numbers 1 and 3 can not appear in the other cells, so they can be eliminated.

Cell H6 contains the numbers (1,9). Number 1 can be eliminated, leaving number 9 as the solution.

The numbers (1,3) can only appear once in the 3x3 box, which results in the elimination of number 1 in cell D5 and F5.

If you scan the column, you will find similar pairs (4,9) in the cells G2 and G3. This will result in the elimination of the numbers 4 and 9 from the cells I1, H2 and H4.

If you find a box containing two similar pairs then these numbers can be eliminated from the other cell in the same box.

Trio's

Scanning for triples is a little bit more complicated because it does not always imply three numbers each in three cells. The cells do not have to contain all numbers of the trio, as long as in combination all three cells have only three numbers.

Example :

  • 3 cells with similar triples
    • cell 1 (3,4,5)
    • cell 2 (3,4,5)
    • cell 3 (3,4,5)
  • 3 cells in combination forming a triple
    • cell 1 (3,4,5) - cell 2 (3,4) - cell 3 (4,5)
    • cell 1 (3,4)    - cell 2 (4,5) - cell 3 (3,5)

Quads

Quads appear seldom in Sudoku puzzles. For quads the same logics as for trio's is applicable.