Links, Chains and Nets

Graph overlays visualise the logical connections between cells used by advanced solving techniques. When the hint system finds a chain-based technique, it displays the reasoning as a graph overlay.

Graph Types

Strong Links

A strong link connects two cells where a digit must appear in exactly one of them. Shown as solid lines.

Weak Links

A weak link connects two cells where a digit cannot appear in both simultaneously. Shown as dashed lines.

Chains

Chains are alternating sequences of strong and weak links that prove eliminations.

Nets

Nets extend chains to multiple branches, used by techniques like 3D Medusa.

Viewing Graphs

Strong links can be displayed by:

Graph overlays also appear automatically when viewing hints for chain-based techniques. Use the hint navigation to step through the chain logic.

Note: A larger update to graph overlays — including a trace feature for interactively following chain logic — is planned for an upcoming release.

Strong Links in Projected Spaces

Strong links are available in projected Berthier spaces (rn, cn, bn). In a projected space, a conjugate pair means a candidate appears in exactly 2 unsolved cells within a row or column of the projected grid.

For example, in rn-space, the link "digit 7 can only go in columns 3 and 8 of row 2" appears as a strong link between cells (R2, D7) at candidates C3 and C8. These are bilocations viewed from a different angle — the projected space makes them visually compact and easy to scan.

To display strong links in a projected space, enter Digit Focus links submode and select a digit.

Related Techniques

Related Features