What is Killer Sudoku? How to Play Killer Sudoku

Killer Sudoku is a Sudoku variant where ‘cages’ (usually outlined by a dotted line or highlighted in different colors) are used as clues instead of given digits in the grid.

These cages will have a number in the upper left corner which tells you the sum of all the numbers in that particular cage.

From this, and in addition to the usual Sudoku rules of every row, column, and 3×3 box containing needing to contain the digits 1 to 9 once each, you will be able to solve the puzzle.

The only additional rule is that the numbers in each cage must all be unique. In other words, no digit can repeat in a particular cage.

Below is an example of a Killer Sudoku puzzle.

Killer Sudoku rules

As already mentioned, the rules of Killer Sudoku are remarkably simple:

• The regular Sudoku rules apply (every row, column, and 3×3 box must contain the numbers 1 to 9 exactly once each
• Numbers must not repeat with any of the killer cages
• The numbers in each cage up sum to value given in the corner of the cage

History

This particular Sudoku variant has been around since the mid-1990s in Japan.

It first became popularized in the English-speaking world when The Times started publishing the puzzles in 2005.

At first, there was ambiguity as to whether the cages had to contain unique digits or if digits could repeat if the regular Sudoku rules allowed it. This was despite it already being the convention in Japan that digits could not repeat within a cage.

Eventually, The Times clarified the rule and it is now standard for Killer Sudoku puzzles around the world not to allow repeated digits within a cage.

Killer Sudoku tips

There are Killer Sudoku puzzles for players of all skill levels. The best advice for when you’re first getting started with Killer puzzles is to start at a lower difficulty level and work your way up.

That said, Killer Sudoku requires additional ways of thinking to solve. So when attempting to solve the puzzles, it can be good to keep the following tips in mind:

1) Start with the cages with the lowest and highest sums.

These cages will be the most restricted in terms of the possible digits they can contain, especially when the cages are made up of a small number of cells.

For example, any one-cell cage must contain the number given as the clue in the upper corner. A two-cell cage with a sum of three must contain the numbers 1 and 2.

A five-cell cage with a sum of 34 must contain the digits 4, 6, 7, 8, and 9. Whereas if the same-sized cell had a total of just 25, there would be twelve potential combinations of digits.

2) The power of 45

As every row, column, and 3×3 box in a Killer Sudoku puzzle must contain the digits 1 to 9, the sum of each of these regions will always be 45. This is known as the rule of 45.

You can use this fact to your advantage when you notice cages are self-contained entirely within one of these regions except for one cell.

To demonstrate this, consider the example puzzle from earlier.

If you look carefully, you’ll notice that the bottom left and right 3×3 regions as well as the center column are all entirely composed of cages that don’t overlap with other regions except for one cell.

As we know that each of these regions must sum to 45, and the sums of the cages are given, we can deduce the value of the lone cells by subtracting the sums of the cages from 45.

For example, in the bottom-left cage we have cages summing to 10, 22, and 4 for a total of 36. This means that the upper-right must be a 9 as 45 – 36 = 9.

We can repeat this in the bottom right cage where there’s another lone cell and all the other cells are covered by cages that sum to 39. Therefore, this remaining cell must contain a 6.

3) Consider the possible combinations of the cages

Each cage can only contain certain combinations of digits based on its size and what value it sums to.

For example, one-cell cages will always be the digit it sums to. Nine-cell cages will always contain the digits from 1 to 9.

While other sized cages will have multiple possibilities, it can be worthwhile keeping a table of them handy when playing Killer Sudoku.

For reference, below is a table of all the possible combinations for the different Killer Sudoku cage sizes.

Where to play

You can play Killer Sudoku places in plenty of places online, including:

Sudoku.com
The Chicago Tribune
BrainBashers