Entropic
Every three consecutive digits contain one from each third of the ordered alphabet. On a two-cell line, the digits come from different thirds.
Parameters
| Parameter | Meaning | Default |
|---|---|---|
| line | The cells in order, for example r1c1-r1c2-r1c3. | Required. |
| loop | Whether the line closes, joining its last cell back to its first. | false (open path). |
Maths
Class: with aggregates.
The shared predicates define the notation and every named predicate.
|𝔄|>0 ∧ |𝔄| mod 3=0
∧ (∀s∈[0,|line|): start(line,3,s,loop) → distinctAt(window(line,3,s,loop),λc:cell: classEntropy(D(c))))
∧ (¬loop ∧ |line|=2 → classEntropy(D(line[0]))!=classEntropy(D(line[1])))
Every window of three path positions has one symbol from each equal-sized third of the ordered board alphabet. An open two-cell line uses different thirds. Loop windows wrap. The alphabet size must be divisible by 3.
Example
---
format: open-rules
title: Entropic example
setter: Example
source: ""
case: ""
library: https://rules.sudoku-sleuth.com/
status: read
---
```rules
sudoku 9x9
entropic r1c1-r1c2-r1c3
```
Satisfies the rule: r1c1=1, r1c2=4, r1c3=7. 1, 4, 7 gives one digit from each of 1–3, 4–6 and 7–9.
Breaks the rule: r1c1=1, r1c2=4, r1c3=6. 1, 4, 6 uses the middle third twice and misses the upper third.