Pressure Gauge
The marked digit counts its listed neighbours that are greater than it for a low gauge, or smaller for a high gauge.
Parameters
| Parameter | Meaning | Default |
|---|---|---|
| type | Low counts larger neighbours; high counts smaller neighbours. | Required. |
| cell | The clue cell. | Required. |
| neighbours | The cells counted or compared around the clue. | Required. |
Maths
Class: with aggregates.
The shared predicates define the notation and every named predicate.
(type="low" → countWhere(neighbours,λc:cell: D(c)>D(cell))=D(cell)) ∧ (type="high" → countWhere(neighbours,λc:cell: D(c)<D(cell))=D(cell))
With n=D(cell), exactly n neighbours are larger than n (low), or smaller than n (high).
Example
---
format: open-rules
title: Pressure Gauge example
setter: Example
source: ""
case: ""
library: https://rules.sudoku-sleuth.com/
status: read
---
```rules
sudoku 9x9
pressure-gauge type "low" cell "r1c1" neighbours ["r1c2","r1c3"]
```
Satisfies the rule: r1c3=1, r1c1=1, r1c2=2. The marked 1 has exactly one larger neighbour.
Breaks the rule: r1c3=3, r1c1=1, r1c2=2. The marked 1 has two larger neighbours.