Killer Sudoku: rules, strategy, and free play
Killer Sudoku is Sudoku with an extra arithmetic layer. You still place digits 1–9 so every row, every column, and every 3×3 box contains each digit exactly once — but the starting grid is empty. Instead of clue cells, the grid is divided into dashed-outline 'cages' that show a target sum. The digits inside each cage must add up to that target and cannot repeat within the cage.
THE RULES
- Standard Sudoku rules apply. Every row, column, and 3×3 box must contain each digit 1–9 exactly once.
- Each cage sums to its target. The number in the cage's top-left corner is the sum of every digit inside the cage. A 3-cell cage marked '12' contains three digits that add to 12.
- No digit repeats within a cage. Even when a row/column would allow a repeat, the cage rule blocks it. A 2-cell cage of 8 can be {1,7}, {2,6}, {3,5} — never {4,4}.
- Starting grids are empty — no pre-placed digits. All your deductions come from the cage sums + the row/column/box rules combined.
BEGINNER STRATEGY
- Memorise unique-sum cages. Some cage size + sum combos have only one possible digit set: a 2-cell cage of 3 is always {1, 2}, a 2-cell of 17 is always {8, 9}, a 3-cell of 6 is always {1, 2, 3}, a 3-cell of 24 is always {7, 8, 9}. These 'magic' combos let you place digits instantly without any standard-Sudoku scanning.
- Use the 45-rule on rows, columns, and boxes. The digits 1–9 sum to 45. If a row, column, or 3×3 box contains cages whose total sum is X with N digits 'spilling out', the spilling cells must sum to 45 − X. Pin one cell and you've often locked a digit.
- Eliminate digits via cage candidates. A 3-cell cage of 7 can be {1, 2, 4} only — so 5, 6, 7, 8, 9 are impossible anywhere in that cage. Cross-reference with the box's remaining digits to narrow placements.
- Treat single-cell cages as direct clues. A 1-cell cage shows the digit literally. Place it and propagate constraints — these are often the only 'free' digits you'll get.
- Never guess. Like classic Sudoku, a legitimate Killer has exactly one valid solution. If you find yourself guessing, look for an unused 45-rule application or an unevaluated unique-sum cage.
COMMON MISTAKES
- Skipping the 45-rule. Most beginners work cage-by-cage and never add up a whole row or box. The 45-rule (digits 1–9 sum to 45 in each unit) is often the fastest deduction on the board — especially when a box has only one "outie" cell.
- Forgetting that cages don't repeat even when rows allow it. The cage no-repeat rule is independent of the Sudoku no-repeat rule. Even if a digit could legally appear in a row and column, it can't appear twice in the same cage.
- Treating a non-unique cage as if it has forced digits. A 2-cell cage summing to 8 has three solutions: {1,7}, {2,6}, {3,5}. Don't place a digit because it 'seems likely' — only place when exactly one candidate survives both the cage constraint and the Sudoku constraints.
- Starting with the largest cages. Large cages (5+ cells) have many digit combinations. Start with 2-cell cages (especially 'magic' sums like 3, 4, 17, 16) and single-cell cages — these give you the most leverage per constraint.
HOW TO THINK ABOUT IT
Killer Sudoku is two puzzles running in parallel: a Sudoku and a Kakuro. The 45-rule bridges them — it lets you reason about the Sudoku unit (row, column, box) using the cage arithmetic, without needing to enumerate individual cage solutions. The best Killer players switch fluidly between scanning for Sudoku constraints and evaluating cage combinations, using whichever layer is most constrained at any given moment.
WHY THIS PUZZLE REWARDS YOU
Killer Sudoku is the puzzle for Sudoku fans who want more depth without changing format. The two-rule system — row/column/box + cage-sum — produces deductions that pure Sudoku and pure Kakuro can't. A typical Killer solve mixes scanning (Sudoku-style) with arithmetic combination work (Kakuro-style), with the 45-rule providing whole-region shortcuts neither parent puzzle has. It's also one of the most asymmetric puzzle types: a 9×9 Killer with 25 cages can be radically harder OR easier than a 'standard' tier of regular Sudoku depending on cage layout.
VARIANTS
- Kakuro. Cage sums without the Sudoku 3×3 box rule — just run sums in a crossword grid. Fewer constraints per cell, but denser arithmetic.
- Calcudoku. Cage arithmetic with + − × ÷ instead of sum-only. The cage no-repeat rule still applies, but the operator changes which digit sets are possible.
- Classic Sudoku. Remove the cages and add pre-filled clue cells. Simpler constraint set — good for a fast warm-up or palate cleanser.
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The Rule of 45 in Killer Sudoku — why it unlocks hard puzzles →
Every row, column, and box sums to 45. Here's how to use that to crack cages that look unsolvable.
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Same grid, same three rules — the real question is which fits where you are as a solver.
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