How to play Killer Sudoku

Killer sudoku hands you an empty grid. Every row, column and three-by-three box still needs the digits one to nine, each used once, exactly as in ordinary sudoku — but not one of those digits is filled in for you at the start.

The clues come as dotted cages instead. Every cage carries a small number in its corner: the sum of whatever digits end up inside it. And one further rule applies — no digit may repeat within a cage, even where the ordinary rules would allow it.

What the dotted lines mean

Each dotted line is drawn round a single cage. The three cells on the left add up to fifteen; the two on the right add up to seven. The small number belongs to the whole cage, not to any one square in it, and the fifteen says nothing at all about the cells beyond its line.

Every square on the board belongs to exactly one cage, so there is always a line on the far side of one — a cage of five squares is the largest you will meet. There is one case where the number is the answer: a cage of a single square has nowhere else to put its total, so that digit is simply given to you. On an Easy board about half the cages are that shape, which is a large part of why Easy is easy.

Why the no-repeat rule matters

Two cells totalling four. It cannot be two and two, because a digit may not repeat inside a cage — so it is one and three, in one order or the other. You have learned two facts before placing anything.

Cages give away more than they seem to, and the small ones give away most. A three-cell cage totalling six holds one, two and three in some order. A two-cell cage totalling seventeen has to be eight and nine. A two-cell cage totalling three is one and two, and there is no other possibility at all.

Four or five certainties like that, written into the grid as pencil marks, and the ordinary sudoku rules start eliminating things for you. This is the whole opening of a killer puzzle: read the cages that can only be one set of digits, then let the rows and columns do the rest.

The rule of forty-five

Every row, every column and every box holds the digits one to nine, so every one of them totals forty-five. That single fact is the technique the harder boards are built around.

Take a box where the cages that fit entirely inside it total forty-one, and one last cage spills over the edge into the box next door. The box needs forty-five. So the cells of that last cage which lie inside the box must supply the missing four, whatever the rest of it is doing. You have just worked out a total that is printed nowhere on the board, and that is the move that gets you through a Hard grid.

How far ahead each difficulty asks you to look

The difficulties are about how far ahead you have to look. The gentler ones give you cages that resolve almost immediately. Harder ones want the rule of forty-five, where a cage that crosses a boundary tells you about the cells it does not cover. Master expects you to hold several of those at once before anything moves.

There is one solution and reasoning always reaches it. When a cage will not give, the row it sits in usually will.

Playing here

Entry works exactly as it does on an ordinary grid — select a cell, then a digit — but pencil marks carry far more weight here. A cage that can only be one and three is two facts you cannot place yet, and writing both into both cells is how you keep them until the row decides for you. Every cage total is printed in the top-left corner of its cage. There is no daily limit and no account.

Play Killer Sudoku