Pairs and Triples in Line

A basic solving method for the elimination of many possible solutions. The following two rules are applicable :

  • If in a box all possible solutions for the same number are on the same row or column, then all possible solutions in the other boxes which are on the same row or column can be eliminated.
  • If in a row (or column) all possible solutions for the same number are in the same box, then all possible solutions in the same box can be eliminated from the other cells.

Example 1 :

theory Y-wing


In this example the number 3 has been found as possible solution for the cells G2 and I2.


Because this number only appears in the cells G2 and I2 and not in other cells in the box, we can conclude that this number will appear as the final solution of the cells G2 or I2. Both cells are on the same row, so the number 3 can not appear on any of the other cells in the same row.


This eliminates the number 3 from the cells A2 and C2.

Example 2 :

theory Y-wing


In this example the number 2 has been found as possible solution for the cells D1 and E1.


Because this number only appears in the cells D1 and E1 and not in any of the other cells in the first row, we can assume that number 2 will be the solution for cell D1 or cell E1. Both cells are on the same row, so the number 2 can not appear in one of the other cells in this row.


This eliminates the number 2 as a possible solution in cell E2, D3 and E3.