N Mate

Count along the ray by the clue digit. That target digit plus the clue equals the cage total. Cage digits are different.

Parameters

Maths

Class: with aggregates.

The shared predicates define the notation and every named predicate.

let n=D(cell); 1<=n<=|ray| ∧ n+D(ray[n-1])=sum_D(cage) ∧ distinct_D(cage)

The marked digit names a one-based position within ray. The marked and target digits sum to the cage total. Cage digits are distinct.

Example

---
format: open-rules
title: N Mate example
setter: Example
source: ""
case: ""
library: https://rules.sudoku-sleuth.com/
status: read
---

```rules
sudoku 9x9
n-mate cell "r1c1" ray ["r1c2","r1c3"] cage ["r1c4"]
```

Satisfies the rule: r1c4=3, r1c1=1, r1c2=2, r1c3=4. The clue and its selected ray digit add up to the cage total.

Breaks the rule: r1c4=4, r1c1=1, r1c2=2, r1c3=4. The selected ray digit gives the wrong total.