Sum Free Cage
Cage digits are different. Adding any two cage digits, including a digit to itself, and taking the stated remainder never produces another cage digit.
Parameters
| Parameter | Meaning | Default |
|---|---|---|
| cells | The marked cells, for example r1c1-r1c2-r2c2. | Required. |
| modulus | The divisor used to take remainders. | Required. modulus ≥ 1. |
Maths
Class: first-order.
The shared predicates define the notation and every named predicate.
modulus>=1 ∧ distinct_D(cells) ∧ ∀a,b,c∈cells: rem(D(a)+D(b),modulus)!=D(c)
Digits are distinct. For every pair of digits a,b in the cage (including a=b), normalised (a+b) modulo modulus is absent from its digit set.
Example
---
format: open-rules
title: Sum Free Cage example
setter: Example
source: ""
case: ""
library: https://rules.sudoku-sleuth.com/
status: read
---
```rules
sudoku 9x9
sum-free-cage r1c1-r1c2 modulus 10
```
Satisfies the rule: r1c1=1, r1c2=3. Adding cage digits never gives a cage digit modulo 10.
Breaks the rule: r1c1=1, r1c2=2. 1 plus 1 gives the cage digit 2.