Cascade

A run of cells resolved by singles once a key cell is placed

How to use it

Not a technique to apply but a beat to read. After a key placement the board often unwinds: cells that were waiting on it resolve as singles, their placements prune their row and column peers, hidden singles take further cells, and so on until the board stalls again. The walkthrough groups such a run into one cascade beat and lets you sub-step through the placements and eliminations in order.

Your job during a cascade is verification, not search: after each placement, check that the next resolution really is forced — the letter had no other home, the digit was the only partner left. When the run stops, the next named technique is waiting.

Why it is sound

Every member of the run is a placement or elimination produced by the trivial techniques (full house, naked and hidden singles, pair singles, peer eliminations after a placement, automatic orthogonality fallout), each individually sound. Grouping them into one beat changes the presentation, not the logic: the cascade's net effect equals the composition of its sound parts.

A worked example

Place the full house B at r4c3 and watch the board unwind on its own: the B is struck from its column-3 peer, which loses its last alternative letter with it and resolves; that placement prunes its row and column peers, a hidden single takes the next cell, and on it goes. The walkthrough gathers the whole run into this single cascade beat — sub-step through it and check that each resolution really is forced. When the run stops, the next named technique is waiting; here a pair-coloring deduction reopens the hunt and a second cascade finishes the job.