Forcing Net

Level 12 · Black Belt

Strategy:

Overview

Forcing Net extends Forcing Chains by following all implications from each candidate simultaneously, not just single chains. This creates a branching implication network that can find deeper contradictions and common outcomes.

How It Works

Find a cell with multiple candidates.
Assume each candidate in turn and follow ALL resulting implications (not just one chain).
If an assumption leads to a contradiction (impossible state), eliminate that candidate.
If all assumptions force the same conclusion, that conclusion is valid.

Example

Starting position

Look for Forcing Net.

Sudoku grid showing the initial puzzle state for Look for Forcing Net.

1

Branch on every candidate of r1c1

Cell r1c1 has 3 candidates: {1, 3, 9}.

Sudoku grid illustrating step 1: Branch on every candidate of r1c1 — Cell r1c1 has 3 candidates: {1, 3, 9}.

2

Assume r1c1 is 1

Assume r1c1 = 1 and follow all implications through the net.

Sudoku grid illustrating step 2: Assume r1c1 is 1 — Assume r1c1 = 1 and follow all implications through the net.

3

This branch leads to a contradiction

This assumption leads to a contradiction, so that branch is impossible.

Sudoku grid illustrating step 3: This branch leads to a contradiction — This assumption leads to a contradiction, so that branch is impossible.

4

Eliminate 1 from r1c1

So 1 causes a contradiction and can be eliminated from r1c1.

Sudoku grid illustrating step 4: Eliminate 1 from r1c1 — So 1 causes a contradiction and can be eliminated from r1c1.

5

Result

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

Forcing Nets are more powerful than Forcing Chains because they follow every implication, not just one path.
They're computationally expensive and are typically a last resort before brute force.
The branching nature makes them hard to track by hand.