The history of Killer

Killer takes Sudoku's grid and throws away its clues. What's left is a puzzle about sums, and it turns out that sums are enough.

From Japan to the newspapers

Puzzles that put sums into a number place grid were already known in Japan by the mid-1990s, under a name that means "sum number place". They reached the English-speaking world in 2005, at the height of the Sudoku craze, when British newspapers began printing them next to their daily Sudoku. There the puzzle got the name it's known by in English: Killer Sudoku, or just Killer.

The name promises a hard time, but it isn't always deserved. With no givens the first glance is daunting; after that, the cages give so much away that an easy Killer can be quicker than an easy Sudoku. The hardest ones, though, live up to it.

The arithmetic of 45

Everything in Killer rests on one fact: 1 + 2 + … + 9 = 45. Since every row, column and box holds each digit once, each of them adds up to 45, and that's what lets a solver work out a cell no cage describes on its own. Players call it the rule of 45, and the cells it reveals innies and outies.

The cages bring a second kind of arithmetic. Cages of two to eight cells can show 119 different sums between them, made from 501 sets of different digits. Only 33 of those sums can be made with just one set — the 3s and 17s that every Killer solver looks for first.

The cousins

• Calcudoku uses cages too, on a grid without boxes, and its cages can multiply, subtract and divide as well as add.
• The number crossword is the other ancestor: there, the sums belong to runs of white cells between black ones, and digits can't repeat within a run.
• Some Killers bend the rules: a few givens to start from, digits allowed to repeat inside a cage, or cages that show a product. Ours keep to the classic form: no givens, and no repeats in a cage.