---
name: Run Sum
url: https://rules.sudoku-sleuth.com/run-sum.md
kind: run-sum
parameters:
  cells:
    description: The marked cells, for example r1c1-r1c2-r2c2.
    default: Required.
    type: list<cell>
  sum:
    description: The total the digits or values must add up to.
    default: Required.
    type: number
---

# Run Sum

Count each digit once when a neighbour along the line differs by 1. These digits add up to the clue.

## Parameters

| Parameter | Meaning | Default |
| --- | --- | --- |
| cells | The marked cells, for example r1c1-r1c2-r2c2. | Required. |
| sum | The total the digits or values must add up to. | Required. |

## Maths

Class: **with aggregates**.

The [shared predicates](https://rules.sudoku-sleuth.com/predicates.md) define the notation and every named predicate.

```text
countRun(cells)=sum
```

Sum each position once when at least one neighbouring position on the line differs by exactly 1. This sum equals sum.

## Example

````markdown
---
format: open-rules
title: Run Sum example
setter: Example
source: ""
case: ""
library: https://rules.sudoku-sleuth.com/
status: read
---

```rules
sudoku 9x9
run-sum r1c1-r1c2-r1c3 sum 6
```
````

Satisfies the rule: r1c1=1, r1c2=2, r1c3=3. All three consecutive-run digits contribute to total 6.

Breaks the rule: r1c1=1, r1c2=2, r1c3=5. A digit outside the run leaves the wrong contributing total.