This walkthrough teaches thinking order—not one puzzle's answer—so you can replay the stages on any well-formed Killer grid. Adapt timings to difficulty; easier puzzles collapse steps together while experts stretch phases longer.
Phase 1 — inventory cages
Scan every sum, highlight extreme tuples automatically (two-cell totals 3,4,16,17), mark ambiguous cages for later.
Phase 2 — pencil candidates
Populate feasible tuples per cage footprint before chasing placements—prevents cherry-picking contradictions.
Phase 3 — Sudoku passes
Run naked/hidden singles across rows—often cages already trimmed candidates enough for instant wins.
Phase 4 — sum wedges
Apply 45 arithmetic along rows/columns/boxes to expose hidden totals or innie/outie deductions.
Phase 5 — alternating loops
Alternate cage tightening with Sudoku subsets until puzzle yields—avoid fixation loops.
Phase 6 — advanced nets
Deploy chains or uniqueness cautiously only after earlier phases stall legitimately.
Verification finale
Re-sum each cage after completion—quick integrity proof.
Adapting phases to puzzle temperament
Aggressive constructors front-load difficult cages—consider reordering phases mentally by prioritizing whichever region exhibits extreme sums first, even if it breaks strictly top-to-bottom habits.
When solves stall mid-phase, rewind one checkpoint rather than restarting blindly—usually the penultimate deduction harbored a transcription drift.
Teaching this walkthrough verbally
Parents guiding kids should narrate phases aloud—kids replicate scaffolding faster than silent demonstrations.
Closing checklist
Confirm each cage satisfied distinctness, each Sudoku unit contains nine digits, and emotional tone stayed curious rather than punitive—healthy solves reinforce persistence.