Yin Yang

Shade the board so each colour forms one connected group and every 2×2 contains both colours.

Parameters

No parameters. It applies to the whole declared board and uses the shared shading answer.

Maths

Class: existential.

The shared predicates define the notation and every named predicate.

connected({c ∈ C: shaded(c)}) ∧ connected({c ∈ C: ¬shaded(c)})
∧ ∀r ∈ [0,rows−1): ∀k ∈ [0,cols−1):
  (∃a ∈ window2(r,k): shaded(a)) ∧ (∃b ∈ window2(r,k): ¬shaded(b))

Both colours are nonempty and orthogonally connected; every 2×2 contains both colours. This is a general authoring-library rule over the one typed shading answer, rather than a newly recognised decoded constraint.

Example

---
format: open-rules
title: Yin Yang example
setter: Example
source: ""
case: ""
library: https://rules.sudoku-sleuth.com/
status: read
board:
  rows: 2
  cols: 2
  symbols:
    - 1
    - 2
    - 3
    - 4
---

```rules
yin-yang
```

Satisfies the rule: r1c1=1, r1c2=2, r2c1=3, r2c2=4; shaded cells r1c1-r1c2. Each colour forms one connected row.

Breaks the rule: r1c1=1, r1c2=2, r2c1=3, r2c2=4; shaded cells r1c1-r2c2. Each colour is separated diagonally.