Remainder Cage
The cage total has the stated remainder after division by the modulus. The distinct parameter forbids repeated digits.
Parameters
| Parameter | Meaning | Default |
|---|---|---|
| cells | The marked cells, for example r1c1-r1c2-r2c2. | Required. |
| modulus | The divisor used to take remainders. | Required. modulus ≥ 1. |
| remainder | The remainder required after division by the modulus. | Required. |
| distinct | Whether repeated digits are forbidden. | Required. |
Maths
Class: with aggregates.
The shared predicates define the notation and every named predicate.
modulus>=1 ∧ rem(sum_D(cells),modulus)=remainder ∧ (distinct → distinct_D(cells))
The normalised remainder of the digit sum modulo modulus equals remainder. If distinct, the digits also differ.
Example
---
format: open-rules
title: Remainder Cage example
setter: Example
source: ""
case: ""
library: https://rules.sudoku-sleuth.com/
status: read
---
```rules
sudoku 9x9
remainder-cage r1c1-r1c2 modulus 3 remainder 1 distinct false
```
Satisfies the rule: r1c1=1, r1c2=3. The total 4 has remainder 1 modulo 3.
Breaks the rule: r1c1=1, r1c2=2. The total 3 has remainder 0 modulo 3.