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Singles in Groups and Cages

The Single in Group and Single in Cage techniques are the most basic method of placing digits in a Killer Sudoku puzzle. The single in group technique is common to regular sudoku. Simply put, if there is only empty cell left in a row, column or box, we can place the appropriate digit in it. An illustration of this is shown below:

In the example above, the cell highlighted in red must be a "1". There is only one cell left to be filled in the top left box. Because no digit can be repeated in any group (any row, column or box), and all the digits except "1" have already been placed in the group, we know that the empty cell must be a "1".

The Single in Cage technique is an extension of this technique specific to Killer Sudoku. If there is only one cell left in a cage, we can place the appropriate digit there. Here is an example:

In this example, we can place a "9" in the red cell. Because the red cell is the only cell in its cage, and the cage must have a sum of 9, the digit "9" is the only valid possibility for this cell. Another example is shown below:

Here, we can put a "2" in the cell highlighted in red. The cell highlighted in red is the only empty cell in the highlighted cage. We know the sum for the cage must be 5, and we already have a "3" in the cage, so the remaining digit must be a "2".

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