Index Line
Count positions from the marked end, starting at 1. A digit X in position N means the digit in position X is N.
Parameters
| Parameter | Meaning | Default |
|---|---|---|
| line | The cells in order, for example r1c1-r1c2-r1c3. | Required. No repeated cell; 2 ≤ n ≤ min(16,|𝔄|). |
Maths
Class: first-order.
The shared predicates define the notation and every named predicate.
∀i ∈ [0,|line|): 1 ≤ D(line[i]) ≤ |line| ∧ D(line[D(line[i])−1])=i+1
Each digit names a one-based position whose digit is the original position. All named positions are within the path. The distinct cells form a self-inverse permutation.
Example
---
format: open-rules
title: Index Line example
setter: Example
source: ""
case: ""
library: https://rules.sudoku-sleuth.com/
status: read
---
```rules
sudoku 9x9
index-line r1c1-r1c2
```
Satisfies the rule: r1c1=2, r1c2=1. Positions 1 and 2 point to each other.
Breaks the rule: r1c1=2, r1c2=2. Position 2 does not point back to position 1.