Region Forcing Net
A Region Forcing Net — also called a House-Digit Forcing Net and traditionally listed as Region Forcing Chain — starts from every remaining position of one digit in a selected house and follows only forced consequences. Because the source alternatives are exhaustive, a conclusion reached by every branch is unconditional.
What is a Region Forcing Net?
A true candidate makes every weakly linked candidate false. A false candidate makes the other side of a strong inference true. False on one side of a weak inference alone proves nothing. A branch choice that is not forced cannot be treated as a consequence. Every remaining source alternative must be tested; one failed branch does not settle the source.
Walkthrough example
A walkthrough of one Region Forcing Net: every remaining position of one digit in a house is tried as a branch, and only a conclusion shared by all branches is applied.
Step 1
Consider these cells.
Step 2
With this solving technique, we will prove the following assertions: 1. If D1 contains the value 2, then F2 must contain the value 3 2. If D4 contains the value 2, then F2 must contain the value 3 3. If D6 contains the value 2, then F2 must contain the value 3 Because the value 2 cannot be placed elsewhere in the column, and the results are the same, we can conclude that F2 must contain the value 3. Each assertion is proved by a different chain of simple rules. The chains are static, which means that each rule of the chain can be understood without having to remember the results of previous rules. Chain 1: 1. If D1 contains the value 2, then D1 cannot contain the value 3 (the cell can contain only one value) 2. If D1 does not contain the value 3, then F2 must contain the value 3 (only remaining possible position in the block) Chain 2: 1. If D4 contains the value 2, then D4 cannot contain the value 4 (the cell can contain only one value) 2. If D4 does not contain the value 4, then D1 must contain the value 4 (only remaining possible position in the column) 3. If D1 contains the value 4, then D1 cannot contain the value 3 (the cell can contain only one value) 4. If D1 does not contain the value 3, then F2 must contain the value 3 (only remaining possible position in the block) Chain 3: 1. If D6 contains the value 2, then D6 cannot contain the value 9 (the cell can contain only one value) 2. If D6 does not contain the value 9, then F6 must contain the value 9 (only remaining possible position in the block) 3. If F6 contains the value 9, then F6 cannot contain the value 3 (the cell can contain only one value) 4. If F6 does not contain the value 3, then F2 must contain the value 3 (only remaining possible position in the column)
Step 3
So values 1 and 9 can be removed from F2: all possible source positions force F2 to contain 3, so no other value can go there.
This walkthrough shows one valid example of the defined deduction. Confirm the stated source set or assumption, that every branch was tested, and that the applied conclusion is shared by all of them before using the same deduction on another grid. You can play sudoku online to practise with the current candidate state visible.
How to spot it
State the source proposition or exhaustive source set, then annotate every step with its reason. Compare all branches and accept only a target truth value shared by every one.
The logic
At least one source alternative is true. If each alternative implies the same target conclusion, the target conclusion holds regardless of which source is true. Optional branches must remain alternatives rather than being reported as forced links.