Killer sudoku is considered one of the most common and well-known sudoku variants. At first glance, a killer sudoku puzzle can appear scary due to the dashed lines and no numbers given on any cell. But it brings another element of standard sudoku due to its arithmetic feature. Now, what are the basic killer sudoku rules?
Basic Rules of Killer Sudoku
At the beginning of the game, you don’t have any numbers given on the grid at all. But the rules are just simple and easy. Like in standard sudoku, you have to place the numbers 1-9 once in each region. The regions/houses are comprised of 9 columns, nine rows, and nine 3×3 bold-lined boxes. You have to make sure that the numbers you place in each cage (dotted-lined region) sum up to the number given at the top-left of that cage. Remember that numbers cannot be repeated within cages.
How do you get the first number in Killer Sudoku?
As mentioned previously, no numbers are given initially except for the ones at the top-left of the cage, representing the sum of the said cage. Now the question is, how do we get the first number in killer sudoku? To start answering this kind of puzzle, first, try to look for cages with only one cell. Yes, it is allowed and possible to have a cage with only one cell. Meaning the number written at the top-left of that cage will be the same number to be placed on that cell.
The next easiest way to start with killer sudoku is to look for sum cages with very low or very high sums. The lower or higher the sum in a specific cage, the fewer possible combinations of numbers there will be. It will help significantly to familiarize yourself with the most popular combinations in order for you to write them straight in without working them out. For example, a two-cell cage with a sum of three must contain the numbers 1 and 2, and a five-cell cage with a sum of 34 must contain the digits 4, 6, 7, 8, and 9. Some other possible and common examples with unique solutions are listed below.
For two-cell cage with only one combination:
Sum | Combination |
3 | 1 and 2 |
4 | 1 and 3 |
16 | 7 and 9 |
17 | 8 and 9 |
For three-cell cage with only one combination:
Sum | Combination |
23 | 6, 8, and 9 |
24 | 7, 8, and 9 |
For four-cell cage with only one combination:
Sum | Combination |
29 | 5, 7, 8, and 9 |
30 | 6, 7, 8, and 9 |
What are the other techniques in solving Killer Sudoku?
Rule of 45
This uses the rule for standard sudoku – every row, column and block must contain each of the numbers 1 to 9 once. Therefore, the sum of all numbers in one row, column or block will always be 45.
In the example above, the sum of the cages in the given row is 43 (13+4+12+14). So, the remaining cell in the row must be 2 (45-43=2). Simple as that.
Innies and outies
Looking at the cages inside a certain region, you often find some only partially located inside or outside that region. Innies are cells that are “poking in”, while outies are cells that are “sticking out”. Several examples of innies and outies are shown below.
This figure is a perfect example of innies. The red square is called a region or house. Inside the region are 7, 9, 13, and 11 as the sum of the cages. By getting their sum, you will get 40. Therefore, the remaining one cell (green circle) in that region is 5 (45-40 = 5).
Another example of innies is shown above. In this case, the region consists of 3 bold-lined boxes. Meaning the total sum of all numbers in the three bold-lined boxes should be 135 (45*3). Then by getting the sum in all cages (13+9+9+9+12+8+15+15+9+14+9+9), we will come up with 131. Therefore, the remaining cell (green circle) is 4 (135-131 = 4).
Moreover, the figure on the left is an example of outies. As said before, this is the cell that sticks out of the house/region (green circle). In this case, the region consists of 3 bold-lined boxes (the sum should be 135 as well). Adding all the cages (21+5+9+15+9+15+11+11+13+10+10+7), we will get 136. Therefore the remaining cell outside the house is 1 (136-135 = 1).
What are you waiting for? Try Killer Sudoku
Even though killer sudoku is a “killer” at a quick look, understanding its fundamental rules and basic tips and techniques (especially the rule of 45) will make this sudoku variant an easy one for you (of course, with the help of constant practice!). And if you desire to enhance your utmost concentration and logical ability, solving killer sudoku is the right path for you. So what are you waiting for? Get your pencil and try one!