Legendary Killer Sudoku — The Hardest Cages

Legendary Killer Sudoku is the top rung of the ladder and the hardest killer sudoku we publish: rated 10.0 and above, with no given digits. Our legendary killers average 10.43, and the hardest killer in the catalogue is rated 12.8. Treat it as a project, not a quick game.

What this level asks

Ordinary logic runs out. Puzzles in this band need the extreme and last-resort tiers: nested forcing chains and contradiction nets built on top of the cage sums. Every legendary killer is verified to have exactly one solution, and that the rater can reach it by logic. A puzzle that needs pure guessing is never published.

With zero givens, everything starts from the cage layout. The opening is the same as at expert: the 45 rule on each row, column and box, then the digits each sum allows. The difference is how soon those run dry. The rule of parity, which looks only at odd and even digits, can still strip candidates from a stubborn cage, but expect to reach chain territory quickly.

Techniques you will meet

• Arithmetic to set the board up: cage splitting, cage compare and the rule of parity.
• Chain tools that carry the rest: alternating inference chains, grouped X-cycles and death blossom.

Tips for this level

• Reduce the board completely first. A chain on a half-reduced board is far longer than it needs to be.
• Expect to use a deep technique more than once in a single puzzle.
• Read about what sits at the top in the hardest sudoku puzzles.

Next step

Not ready? Master Killer is one band down. Come back to legendary once master grids feel routine, and bring patience: a single puzzle can fill a whole session, and progress is saved so you can stop and resume whenever you need.