Oriented Chains

Oriented chains are generalisations of the basic xy‑chains.

The central idea is that the information collected from previous candidates in a chain (and/or from the target) can be used to select the next candidates. Oriented chains are either 2‑D or 3‑D:

• Oriented 2‑D chains: xyt‑chains, xyz‑chains and xyzt‑chains, together with their hidden counterparts: hxyt‑chains, hxyz‑chains and hxyzt‑chains;
• Oriented 3D chains: nrct‑chains, nrcz‑chains, nrczt‑chains.

(The original reference to all these chains is the book The Hidden Logic of Sudoku. Further web references forthcoming.)