Killer Sudoku

Basic Solving Strategies

The following are the basic rules used to solve killer sudokus.

Rule of 1

This comes directly from the definition of sudoku. No region can contain any duplicate digits. In a sudoku region each digit appears exactly once. For example, if a digit appears in a row, it cannot be in any other cell in the row. Likewise, each digit can appear in a cage only once. If a digit is in a cage, it cannot appear in that cage again.

Rule of Necessity

This rule can be applied to sudoku regions (i.e., row, column, or nonet) or to a cage. In the former case, each region must contain all the digits one to nine. Thus, if all the digits but one appear in a row, the missing digit must appear in the empty cell.

Rule of 45

Each sudoku region (i.e., row, column, or nonet) contains the digits one through nine. Thus, each sudoku region has a total value of 45. If S is the sum of all the cages contained entirely in a region, then the cells not covered must sum to 45-S.

Rule of K

The Rule-of-k is an extension of the Rule-of-1. If there are k cells contained entirely in a region that contain exactly k different possible values, then no other cell in that region can contain any of those k values.

Sum Elimination

This strategy examines the different possible ways of making the sum of a cage. Reducing the number of different possible ways of making a sum, can often lead to a potential solution. There are many ways of reducing the number of sums. For example, if a 2-cage has a total of 3, 4, 16, or 17 there is only one combination of values that can be used. (3=2+1, 4=3+1, 16=9+7, and 17=9+8.) 3-cages with only 1 combination are: 6=1+2+3, 7=1+2+4, 23=9+8+6, 24=9+8+7. The sum calculator found in the online player page can be very handy.

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Applying the basic strategies. An Example

Here we will use the above strategies to solve a puzzle. You might want to print out the puzzle so you can follow along all the steps.

Rule of 45
Rule of necessity
Rule of 1
Unique Sums
Rule of K
Rule of K Limited possible sums
Rule of necessity
Limited Possible Sums
Rule of K
Limited Possible Sums Rule of 1 Rule of K
Rule of Necessity Rule of 1 All Possible Sums
Rule of Necessity Limited possible sums
Rule of K Rule of 1 Limited Possible Sums
Remaining sum Rule of 1 Rule of K Rule of necessity
Sum Elimination
Sum elimination Rule of 1
Range of Totals Sum Elimination
Rule of 1 Rule of necessity Remaining Sum
Limited possible sums Rule of 1 Rule of necessity
Rule of necessity Rule of 1

Sample Sum, You try...

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