---
name: Window Classes
url: https://rules.sudoku-sleuth.com/window-classes.md
kind: window-classes
parameters:
  classes:
    description: "The digit classes to use: parity, remainder or alphabet thirds."
    default: Required.
    type: ClassSystem
---

# Window Classes

Every two-by-two window contains every stated digit class.

## Parameters

| Parameter | Meaning | Default |
| --- | --- | --- |
| classes | The digit classes to use: parity, remainder or alphabet thirds. | Required. |

## Maths

Class: **first-order**.

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

```text
(classes!="entropy" ∨ (|𝔄|>0 ∧ |𝔄| mod 3=0)) ∧ ∀r∈[0,rows-1): ∀k∈[0,cols-1): ∀j∈classIds(classes): ∃c∈window2(r,k): digitClass(classes,D(c))=j
```

Every 2×2 board window contains all classes named by classes at least once.

## Example

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

```rules
sudoku 9x9
window-classes classes "parity"
```
````

Satisfies the rule: r1c1=1, r1c2=2, r2c1=4, r2c2=5. This two-by-two window includes both parities.

Breaks the rule: r1c1=1, r1c2=3, r2c1=5, r2c2=7. A two-by-two window contains only odd digits.