The 45 Rule in Sudoku is a Killer Sudoku strategy that uses one simple fact: The numbers 1 to 9 add up to 45\. Because every row, column, and 3x3 block must contain those nine numbers with no repeats, you already know that every complete unit in a Sudoku grid has a total value of 45.

That known total becomes especially useful in [Killer Sudoku](https://sudokubliss.com/killer). Killer Sudoku follows the same basic [Sudoku rules](https://sudokubliss.com/guides/how-to-play) as the classic version, but it also groups cells into cages with sums shown in the upper-left corner. That’s why the rule works for Killer, not Classic, Sudoku. Because you know the sum of those cages even when you haven't solved the individual cells, you can compare the cage sums, givens, and placed candidates in a unit with 45 to figure out what's missing.

In some cases, the Rule of 45 lets you place a candidate immediately. In others, it narrows the possible candidates so you can combine that information with other Sudoku techniques. Either way, it can help you make progress without having to solve every individual cell first when you [play Sudoku online](https://sudokubliss.com/).

## Understanding the 45 Rule for a Killer Sudoku Puzzle

The Rule of 45 depends on where cages are placed. Some cages span multiple units, and the cells that cross the boundary of the area you're totaling are called _innies_ and _outies_:

* An **innie** extends into the unit you're calculating or targeting. For example, if you add all the cage sums and answers in a unit that contains an innie and they equal 38, you simply subtract that number from 45 and can place 8 in the innie cell.
* An **outie** extends beyond the unit you're calculating or targeting. For example, if the cages and answers in a unit add up to 52 because one of the cages extends into another unit, then you subtract 45 from that total and can place 7 in the outie cell.
![Sudoku grids showing the difference between innies and outies for the 45 Rule for Sudoku](https://sudokubliss.com/content-uploads/difference-between-innies-and-outies-for-45-Rule-sudoku.webp)  

## How to Use the 45 Rule to Place a Candidate

Follow these steps to use the 45 Rule to place a candidate:

1. **Target an innie cell that has the rest of its cage outside of the unit (row, column, or block).** If only one cell in a row, column, or block has a cage outside of that unit, it’s a good target for the 45 Rule. For example, D9 is the only cell in the bottom middle block with a cage extending outside of that unit.
2. **Find the sum of all the givens, placed candidates, and cages in the unit.** You don’t need to solve all the other cells in the unit or even most of them to use the rule because you can use the cage sums instead. For example, the givens (9+3), plus the placed candidate (5), plus the only two remaining cages (13+7) total 37\. You now know the total of all the cells except the target cell (D9).
3. **Subtract the number from step 2 from 45 and place candidates.** The digits placed in the 3x3 block must equal 45\. So just do simple math and subtract from 45 the total you found in step 2\. For example, the difference between 45 and 37 is 8, so D9 must be 8.
![Sudoku grid example showing how to use the 45 Rule for Sudoku to place a candidate](https://sudokubliss.com/content-uploads/how-to-use-sudoku-45-Rule-to-place-a-candidate.webp)  

## How to Use the 45 Rule to Eliminate a Candidate

Follow these steps to use the 45 Rule to eliminate a candidate:

1. **Target a unit with three or fewer innies.** A unit with just two innies is a perfect target. For example, the top-middle block has two innies (D1 and D3).
2. **Find the sum of all the givens, placed candidates, and cages in the unit.** You don’t need any solved cells to do this technique, so it’s an excellent first step to narrow down candidates in a Killer Sudoku puzzle. For example, you can add all the cage sums in the block (9+10+17) for a total of 36.
3. **Subtract the number from step 2 from 45 and determine possibilities.** The digits placed in the 3x3 block must equal 45, and the difference between 45 and 36 is 9\. So the two innies must have placements that equal 9, and pairs that equal 9 include:  
  * 1, 8
  * 2, 7
  * 3, 6
  * 4, 5
4. **Eliminate candidates that can’t be possibilities.** In this example, you can eliminate any pair that doesn’t appear split between the cells.  
  * Because D1 has a 1 but D3 doesn’t have an 8, you can eliminate the 1 in D1.
  * Because neither D1 or D3 has a 6 or a 2, the pairs 2 and 7 and 3 and 6 can’t be answers for those cells. So the 3s can be eliminated from D1 and D3, and 7 can be eliminated from D3.
  * This leaves 4, 5, and 8 as candidates in D1 and 1, 4, and 5 as candidates in D3.
![Sudoku grid example showing how to use the 45 Rule for Sudoku to eliminate candidates](https://sudokubliss.com/content-uploads/how-to-use-the-45-rule-to-eliminate-a-candidate.webp)  

## Additional 45 Rule Examples

The first examples are innies, which are the most common way you’ll use the Rule of 45, but the final example is an outie.

### Sudoku 45 Rule Used in a Column

Follow these steps to use the 45 Rule in a column:

1. **Target an innie cell that has the rest of its cage outside of the column.** For example, B1 is the only cell in column B with a cage outside of that unit.
2. **Find the sum of all the givens, placed candidates, and cages in the column.** In this example, because some cages are only partially solved, it’s easier to just add the cage sums in that column except for B1 (5+22+15). So the total of all cage sums in that column except B1 is 42.
3. **Subtract the number from step 2 from 45 and place or eliminate candidates.** For example, the difference between 45 and 42 is 3, so B1 must be 3.
![Sudoku grid example showing how to use the 45 Rule for Sudoku in a column](https://sudokubliss.com/content-uploads/using-45-rule-in-a-column-example.webp)  

### Sudoku 45 Rule Used in a Row

Follow these steps to use the 45 Rule in a row:

1. **Target an innie cell that has the rest of its cage outside of the row.** For example, C7 is the only unsolved cell in row 7 with a cage outside of that unit.
2. **Find the sum of all the givens, placed candidates, and cages in the row.** For example, the givens (6+1+3), plus placed candidates (5+7+9), and plus the only cage left (10) equal 41.
3. **Subtract the number from step 2 from 45 and place or eliminate candidates.** For example, the difference between 45 and 41 is 4, so C7 must be 4.
![Sudoku grid example showing how to use the 45 Rule for Sudoku in a row](https://sudokubliss.com/content-uploads/how-to-use-45 Rule-in-a-row-example.webp)  

### Sudoku 45 Rule Used in a Block

Follow these steps to use the 45 Rule in a block:

1. **Target an innie cell that has the rest of its cage outside of the block.** For example, D8 is the only unsolved cell in the middle-bottom block with a cage outside of that unit.
2. **Find the sum of all the givens, placed candidates, and cages in the block.** For example, the givens (1), plus placed candidates (7), and plus the cages (10+9+13) equal 40.
3. **Subtract the number from step 2 from 45 and place or eliminate candidates.** For example, the difference between 45 and 40 is 5, so D8 must be 5.
![Sudoku grid example showing how to use the 45 Rule for Sudoku in a block](https://sudokubliss.com/content-uploads/using-the-45-Rule-in-a-block-example.webp)  

### Sudoku 45 Rule Outie Example

Follow these steps to use the 45 Rule for an outie:

1. **Target an outie cell that has the rest of its cage inside a unit.** For example, A6 is the only unsolved cell in its cage that extends out of the bottom-left block.
2. **Find the sum of all the givens, placed candidates, and cages in the block plus the outie cage.** For example, the givens, answers, and cage sums in the bottom-left block add up to 38 (13+15+1+3+6). So using the rule of 45 (45−38), A7, the only cell not included in the sum, must be 7.
3. **Use your answer from step 2 to place or eliminate candidates.** For example, because we determined the other cell’s answer (7 in A7) that shares the cage with the outie, we know that A6 must be 3 so that the cage value equals 10.
![Sudoku grid example showing how to use the 45 Rule for Sudoku with an outie](https://sudokubliss.com/content-uploads/using-the-45-Rule-in-an-outie-example.webp)  

The 45 Rule is a powerful Sudoku technique when solving Killer Sudoku grids. You don’t even need pencil marks or candidates to quickly move through cage combinations, do the math, and place candidates in cells. You can practice this method and play a variety of levels of Killer Sudoku whenever you [play Killer Sudoku online](https://sudokubliss.com/killer) at Solitaire Bliss.