Molecules
Electron digits around each atom add up to its stated total. All cells at or below the electron threshold are electrons; higher digits may also be chosen. Touching atoms share the same electron choices.
Parameters
| Parameter | Meaning | Default |
|---|---|---|
| atoms | The electron cells touching each atom, one list per atom. | Required. |
| sum | The total the digits or values must add up to. | Required. |
| electronMax | Every digit at or below this number must be an electron. | Required. |
Maths
Class: existential.
The shared predicates define the notation and every named predicate.
∃E:set<cell>: E⊆allCells(atoms)
∧ (∀c∈allCells(atoms): D(c)<=electronMax → c∈E)
∧ (∀A∈atoms: sum_D(A∩E)=sum)
There is one Boolean electron choice per cell shared by every atom touching it. Cells with D(c) ≤ electronMax are electrons. Each atom’s electron digits sum to sum; higher digits may be electrons or not.
Example
---
format: open-rules
title: Molecules example
setter: Example
source: ""
case: ""
library: https://rules.sudoku-sleuth.com/
status: read
---
```rules
sudoku 9x9
molecules atoms [["r1c1","r1c2"]] sum 3 electronMax 2
```
Satisfies the rule: r1c1=1, r1c2=2. Electron digits 1 and 2 total 3.
Breaks the rule: r1c1=2, r1c2=2. The two required electron digits 2 total 4.