How to solve Killer Sudoku
Killer Sudoku is a sudoku that starts with no digits at all. In their place the grid is cut into cages, each with a small sum in its corner: the digits of a cage add up to that sum, and no digit repeats inside a cage. Every row, column and 3 × 3 box still holds 1 to 9 once.
Almost every move here comes from two facts: how many ways a sum can be made from different digits, and that a whole row, column or box always adds up to 45. This page walks through the most common moves in turn, simplest first, each on a board you can click through at your own pace.
How to play
Fill the grid so every row, every column and every 3 × 3 box holds the digits 1–9, each exactly once.
The dashed outlines are cages: the digits in a cage add up to the small number in its corner, and no digit repeats within a cage.
No digit is given. The sums are enough: there is exactly one solution, and it never needs a guess.
Tap a cell and pick a digit on the pad under the board; the same digit again clears it. With notes on, digits are pencilled small in the cell instead. Under the pad: the selected cage’s combinations, and a calculator for adding up sums.
A reddish cell holds a digit its row, column, box or cage already has, or sits in a cage whose sum has gone wrong; a cage’s sum and outline grey out once it is done.
The cages and their sums are the whole puzzle; every digit is yours to write. Every board has exactly one solution and can be reached without guessing. The usual sudoku moves work here too — a digit with only one place left in a row, a cell with only one digit left — and the cages add moves of their own.
Sure cages
Most sums can be made from different digits in several ways, but the two smallest and the two largest for each number of cells in only one. Two cells make at least 3 (1 + 2) and at most 17 (8 + 9); three cells at least 6 and at most 24. Such a cage says at once which digits it holds, though not yet where.
A cage in one row
When a whole cage lies in one row, column or box, the digits it must hold are spoken for there: no other cell of that row, column or box can take them. Two or three cages like that often leave the rest of the row only a few digits to share.
The rule of 45
A row holds every digit from 1 to 9 once, so its digits always add up to 1 + 2 + … + 9 = 45 — and so do a column’s and a box’s. Take away the cages lying wholly inside, and whatever is left over has to make up the difference. This is the move that opens most Killer Sudokus.
Cells that stick out
The rule of 45 works the other way too. Take every cage with a cell in a row, column or box, even the ones that stick out of it: together they add up to more than 45, and the extra is exactly what the cells sticking out hold.
45 over two rows
On the hardest boards a single row often leaves too much over, but two rows together can leave just one cell. Two rows hold 1 to 9 twice, 90 in all; three rows 135. The same goes for neighbouring columns and for two boxes side by side.
No timer. Leave and come back — it’s saved.
Play today’s Killer Sudoku