In the Cell Forcing Chain strategy we build chains alternating Strong Links (also see note at the bottom of this page) and Weak Links starting from each candidate in a particular Cell. All chains start with the candidate "ON".

FORCING CELL Type 1 (always "ON") : all chains meet in a Cell with the same candidate "ON". This candidate must be the solution for that Cell, as it is always "ON" whichever the solution for the starting Cell of the chain.

Here, A3 must have either 1, or 2, or 6 as solution.

• if 1 is the solution, the magenta chain implies that 5 is the solution in A6
• similarly, if 2 is the solution, the blue chain implies that 5 is the solution in A6
• finally, if 6 is the solution, the red chain implies that 5 is the solution in A6

FORCING CELL Type 2 (always "OFF") : all chains meet in a Cell with the same candidate "OFF". This candidate can not be the solution for that Cell, as it is always "OFF" whichever the solution for the starting Cell of the chain.

In this example if candidate 1 is the solution in F4, then the blue Chain implies that candidate 1 can not be the solution in A2.
If candidate 3 is the solution in F4, then the pink Chain implies that candidate 1 can not be the solution in A2.
Whichever the solution in F4, candidate 1 can not be the solution in A2. It can be eliminated in A2.

FORCING CELL Type 3 (some candidates "ON" in one Cell) : all chains meet in a Cell with some candidates "ON". As one of the chains identifies the solution for all its Nodes and as we have built all possible chains, the candidates "ON" in the ending Cell are the only possible solutions for that Cell. Hence the other candidates in that Cell can not be the solution.

FORCING CELL Type 4 (some candidates "ON" in a region) : all chains set the same candidate "ON" in the same region (Row, Column or Square). As one of the chains identifies the solution for all its Nodes and as we have built all possible chains, the candidate can not be the solution in any other Cell of that region.

In this example if candidate 5 is the solution in C8, then the pink Chain implies that candidate 5 must be the solution either in H4, or in H5.
If candidate 9 is the solution in C8, then the blue Chain implies that candidate 5 must be the solution either in G5, or in H5.
Whichever the solution in C8, candidate 5 can not be the solution in G4. It can be eliminated in G4.

NB: more formally, a Strong Link is the relationship that exists between two Cells in a region (Row, Column or Square) when these two Cells are the only Cells in that region that contain a particular candidate: if the candidate is not the solution for the first Cell, then it must be the solution for the second Cell, and vice-versa.
However, in the Chaining Strategies, we consider Strong Links as links going from a Cell or a group of Cells where we assert the candidate is not the solution (we say the candidate is in the "OFF" state) to a Cell or a group of Cells where it then must be the solution (we say the candidate is in the "ON" state).
If we consider a Bi-Value Cell, asserting that one of its candidates is not the solution implies that the other candidate must be the solution. Hence there also exists a Strong Link between the two candidates of a "Bi-Value" Cell.

A Weak Link as a link going from a Cell/group of Cells where the candidate is "ON" to a Cell/group of Cells where it is "OFF".

You can practice this strategy by installing the SudokuCoach application on your Android™ device.