Every solving method, organised by what it works on

Splitting one clue sentence into its separate, independent facts before you act on any of them.

Noticing that almost any clue naming two different items, in different categories, also tells you those two items belong to different subjects.

Marking a clue exactly as it is written, with no further reasoning required.

Reading an either/or clue for the one thing it gives you immediately: the two alternatives can't be the same subject.

Reading a comparative clue for the extremes it rules out, not just the comparison itself.

Reading an offset or gap clue for every value that has no valid partner at the required distance, not just the pair it directly restricts.

Reading a 'one of these' clue as a statement about everyone outside the named set, not just the set itself.

Reading a conditional clue backwards: if the consequence is false, the trigger must be false too.

Writing down a fact the clue gives you that has nowhere to go on the board yet.

Turning a clue that refers to an attribute rather than a name — gender, nationality, a preamble fact — into a concrete candidate list before doing anything else.

The moment you confirm one pairing, every other pairing that competes with it in the same row or column becomes impossible.

When every option but one in a row or column has been eliminated, the survivor must be true, even if no clue ever said so directly.

Carrying a confirmed fact from one mini-grid into another that shares a category with it.

Carrying a confirmed elimination from one mini-grid into another that shares a category with it.

When two items are each confined to the same two subjects, those two subjects are used up between them, so everyone and everything else is excluded from both.

The same idea as a locked pair, extended to three or more items: if k items between them can only reach k possibilities, those k possibilities belong to them.

The locked-pair idea applied across categories: if a locked pair in one mini-grid lines up with a locked pair in another, the two pairs' possible subjects are the same set.

The pigeonhole check behind every locked-set deduction: if m items are confined to fewer than m possibilities, the puzzle has contradicted itself, and if they are confined to exactly m, that is a locked set.

The moment one whole category is resolved, transposing every one of its facts into every other mini-grid before doing anything else.

If nothing in a third category can connect two items, they cannot be paired with each other.

Linking several comparative clues together into one ordered chain, so each new link tightens both ends.

Combining two comparative or offset clues that share a reference point into a new deduction neither clue gives up alone.

The moment one branch of an either/or clue is disproved, the other branch becomes true.

When two either/or clues share one half, and their other halves contradict each other, the shared half must be true.

Two exact-offset clues with the same step size lock their subjects into a pair that moves together across the ordered category.

Firing a conditional clue: forward when its trigger becomes true, backward (see Contrapositive Reading) when its consequence becomes false.

Combining two off-grid facts from your ledger into a deduction that finally lands on the board.

Two clues that individually say nothing about two particular items can, taken together, force those two items apart.

The order to work in: harvest every static clue first, sweep the grid, then re-read only the clues that were still dynamic.

Marking each clue, as you use it, as either fully spent or still waiting on the board.

Keeping the off-grid notes tidy: adding a fact when a clue cannot be marked, and crossing it off once it finally lands on the board.

When several places on the board could be worked next, choosing the one with the fewest remaining possibilities.

Assuming one cell is true, following the consequences through, and treating a contradiction as proof the assumption was false.

Systematic, disciplined branching: pick an arbitrary but recorded starting point, follow it to either a solution or a contradiction, and unwind cleanly if it fails.

The fixed four-sweep checklist for when nothing is moving: grid sweep, re-read dynamic clues, ledger sweep, then re-check the ordered categories' boundaries.