Forcing Chain

Index
Dual Implication Chain
The Forcing Chain technique can be used to find the value of a cell making a chain of pairs. This technique is also known as Double Implication Chains because two chains are involved. How this technique can be used is explained in two examples.

  • When cell AB is an 8, cell A1 is an 1 and the yellow cell a 7.
  • When cell AB is an 2, cell B1 is a 4, cell B2 a 1, cell B3 a 5, cell B4 a 2, cell B5 a 7, cell B6 a 1 and the yellow cell a 7.
Whichever value cell AB has, the yellow marked cell has the value 7. This value can be assigned safely.
Forcing Chain
It is not allways possible to assign a value using this technique. In the following example a candidate value is excluded using Forcing Chains.
  • When cell AB is a 3, cell A1 is a 7, cell A2 a 9 and the yellow marked cell is not a 9.
  • When cell AB is a 5, cell B1 is a 4, cell B2 a 5, cell B3 a 9 and the yellow marked cell is not a 9.
Whichever value cell AB has, the yellow marked cell can not have the value 9. This value can be excluded safely.
Forcing Chain
Triple Implication Chain
In the example below, three chains are used to exlude candidate 3 from the yellow highlighted cell.
  • When cell ABC is a 4, cell A1 is a 3, and the yellow marked cell is not a 3.
  • When cell ABC is a 2, cell B1 is a 3, and the yellow marked cell is not a 3.
  • When cell ABC is a 6, cell C1 is a 2, cell C2 is a 3, and the yellow marked cell is not a 3.
Whichever value cell ABC has, the yellow marked cell can not be 3. This value can be exludes safely.
Forcing Chain