---
name: Palindrome
url: https://rules.sudoku-sleuth.com/palindrome.md
kind: palindrome
parameters:
  line:
    description: The cells in order, for example r1c1-r1c2-r1c3.
    default: Required.
    type: path<cell>
---

# Palindrome

The values along the line read the same forwards and backwards.

## Parameters

| Parameter | Meaning | Default |
| --- | --- | --- |
| line | The cells in order, for example r1c1-r1c2-r1c3. | Required. |

## Maths

Class: **first-order**.

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

```text
∀i ∈ [0,|line|): V(line[i]) = V(line[mirror(line,i)])
```

Positions at equal distances from opposite ends have equal values.

## Example

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

```rules
sudoku 9x9
palindrome r1c1-r1c2-r2c3-r2c4-r3c4
```
````

Satisfies the rule: r1c1=1, r1c2=2, r2c3=3, r2c4=2, r3c4=1. 1, 2, 3, 2, 1 reads the same from either end.

Breaks the rule: r1c1=1, r1c2=2, r2c3=3, r2c4=2, r3c4=4. 1, 2, 3, 2, 4 has different end digits.