How to Play Killer Sudoku — Cages, Sums and the Rule of 45

Cubedoku Guides · Published 2026-06-10

Killer Sudoku is what happens when Sudoku and Kakuro have a child: the familiar grid and rules, plus dotted-line regions called cages, each labelled with the sum of the digits inside it. It is arguably the most popular Sudoku variant in the world — and unlike many variants, it usually starts with no given digits at all. Every placement is earned through arithmetic and logic working together.

The rules

  • All classic Sudoku rules apply: every row, column and box contains each digit exactly once. (New to those? Start with the Classic guide.)
  • The grid is fully covered by cages— outlined groups of two to five (occasionally more) cells. The small number in a cage's corner is the sum of the digits it contains.
  • No digit repeats inside a cage — even when the cage spans two rows or boxes. A 2-cell cage summing to 8 can be 1+7, 2+6 or 3+5, but never 4+4.

The cage combinations that do the work

The heart of killer solving is knowing which digit sets can make a sum. The extremes are gold, because they are unique:

  • A 2-cell cage of 3 is forced: {1,2}. A 2-cell cage of 17 is forced: {8,9}. (4 = {1,3}, 16 = {7,9} — also unique.)
  • A 3-cell cage of 6 must be {1,2,3}; of 24 must be {7,8,9}.
  • A 4-cell cage of 10 must be {1,2,3,4}; of 30 must be {6,7,8,9}.

Mid-range sums have several candidate sets, but even those carry information: a 2-cell cage of 5 ({1,4} or {2,3}) can never contain a digit above 4. Treat each cage's possible sets as candidates and intersect them with ordinary Sudoku eliminations — that interplay is the game.

The rule of 45

The signature killer technique. On a 9×9 grid, every row, column and box contains 1 through 9, which sum to 45. So:

  • If the cages inside one box sum to 45 but one cell of those cages pokes outsidethe box, that outie cell equals the cages' total minus 45.
  • If cages cover a box except one cell, that inniecell equals 45 minus the cages' total.

Experienced solvers extend this to two or three rows at once (90, 135…) to crack openings where no cage is unique. On other grid sizes the constant changes but the idea is identical — a 6×6 line sums to 21, a 16×16 line to 136 — “rule of 45” is just its 9×9 name.

A sensible solving routine

  1. Mark the forced cages first. Scan the whole grid for unique-combination sums (3, 4, 16, 17 on pairs; 6, 7, 23, 24 on triples). Pencil their digit sets in.
  2. Run innies and outieson every box and on the grid's corners, where cages tile awkwardly and single cells get forced.
  3. Switch hats constantly.After every arithmetic deduction, do a round of ordinary Sudoku scanning — a placed digit shrinks neighbouring cages' combinations, which forces more digits, and so on.
  4. Watch cage shapes. A cage folded inside one box obeys box-uniqueness automatically; a straight cage along a row additionally blocks those digits for the whole row. Shape is information.

Why killer is great brain training

Killer adds light mental arithmetic to everything classic Sudoku already trains — working memory, scanning, elimination — which is why many players find it the most satisfying variant of all: two different kinds of thinking confirming each other. If you enjoy the brain-training angle of puzzles, killer is the natural next step after mastering intermediate techniques.

Killer Sudoku in Cubedoku

Cubedoku's Killer mode builds on the same engine as Classic, with cages and sum clues on grids from 6×6 up to 25×25 — the 6×6 is a gentle introduction to cage arithmetic, while a 25×25 killer is one of the most demanding solves in the game. Every puzzle keeps the same guarantee as the rest of Cubedoku: exactly one solution, reachable by logic alone, so every cage deduction you make is sound. If the arithmetic layer ever feels heavy, drop back to Classic mode to keep your row-column-box instincts sharp, then return.

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