sudoku.day

Solving techniques

Every puzzle here is graded by the techniques needed to finish it — no guessing, ever. Each entry below explains one move and shows it on a real board, frozen at the moment the move applies. The hint button in a puzzle points at these same moves.

Techniques for every sudoku

These work in any sudoku, classic or killer: every row, column, and 3×3 box contains the digits 1–9 exactly once, and everything below follows from that single rule.

Easy

  1. naked single — A cell has only one candidate left.
  2. hidden single — A digit has only one possible home in a unit.

Medium

  1. naked subsets — Pairs or triples that lock digits out of a unit.
  2. hidden subsets — Digits confined to as many cells lock those cells.

Hard

  1. intersection — Pointing/claiming between a box and a line.

Expert

  1. x-wing — A digit in two rows aligned on two columns (or vice versa).
  2. swordfish — Three-line fish: a digit confined to a 3x3 line pattern.
  3. xy-wing — Three bivalue cells forcing a distant elimination.
  4. jellyfish — Four-line fish: a digit confined to a 4x4 line pattern.

Killer sudoku adds cages

Killer sudoku starts with a completely empty grid. Instead of given digits, the grid is carved into outlined groups of cells called cages, and each cage shows the total its digits must add up to. Those sums are the only clues; everything else is deduction.

  • The digits in a cage add up to the sum printed in its corner.
  • A digit never repeats inside a cage.
  • Every row, column, and box adds to 45 — comparing that fixed total against the cage sums inside it (the “45-rule”) reveals cells the cages alone don’t show.

All the universal techniques above still apply. On top of them, cage arithmetic opens moves of its own:

Medium

  1. cage combinations — A cage's sum rules out candidate digits.
  2. 45-rule (unit) — Innies/outies of a single row, column, or box.
  3. cage/unit overlap — A digit every cage sum requires, confined to one unit, leaves the rest of it.

Hard

  1. cage no-repeat — A digit confined to one cage within a unit leaves the cage's other cells.
  2. 45-rule (multi) — Innies/outies across 2-4 stacked row/column bands.
  3. cage splitting — A unit's innies pin part of a cage's sum, splitting it into two known cages.
  4. innie/outie difference — An innie and an outie whose difference is fixed by the 45-rule.