Math Puzzle — 5×5 KenKen-style Latin

What this is?

One-file, pure JS + JSON solver for a 5×5 KenKen-style Latin puzzle. Edit the JSON, then click Run ARC.

Data — grid N=5 and cages. A cage has an operator (= + - × ÷) and a target applied to its cells.
Policies — declarative constraint families: row/column all-different and cage arithmetic.
Answer — newly derived facts (the solved digits), with a checks summary.
Reason Why — mathematical-English explanations per cage and row/column uniqueness.
Check — auto-generated assertions (rows, columns, cages): … items.

Engine: domain propagation (1..N), cage tuple filtering, Latin all-different, and DFS backtracking. Works well up to N≈6 for typical puzzles.

Puzzle Details

Size: 5×5 (values 1..5). Latin rule: each row/column has each number exactly once.
Operators: = (singleton), + (sum), - (absolute diff, two cells), × (product), ÷ (integer division, two cells, no remainder).
Design: Mixed singletons, sum pairs, and difference pairs for medium difficulty.
Editing: You can alter size (2..6) and cages. Ensure every cell appears in exactly one cage.
Tip: Singletons seed values; all-different prunes domains; cages do arithmetic pruning; backtracking finishes.

Data (JSON)

{
  "size": 5,
  "cages": [
    { "id": "A", "op": "+", "target": 3,  "cells": [ [1,1], [1,2] ] },
    { "id": "B", "op": "=", "target": 3,  "cells": [ [1,3] ] },
    { "id": "C", "op": "-", "target": 1,  "cells": [ [1,4], [2,4] ] },
    { "id": "D", "op": "+", "target": 6,  "cells": [ [1,5], [2,5] ] },
    { "id": "E", "op": "=", "target": 2,  "cells": [ [2,1] ] },
    { "id": "F", "op": "+", "target": 7,  "cells": [ [2,2], [3,2] ] },
    { "id": "G", "op": "+", "target": 9,  "cells": [ [2,3], [3,3] ] },
    { "id": "H", "op": "-", "target": 1,  "cells": [ [3,1], [4,1] ] },
    { "id": "I", "op": "+", "target": 3,  "cells": [ [3,4], [3,5] ] },
    { "id": "J", "op": "+", "target": 6,  "cells": [ [4,2], [4,3] ] },
    { "id": "K", "op": "=", "target": 2,  "cells": [ [4,4] ] },
    { "id": "L", "op": "-", "target": 1,  "cells": [ [4,5], [5,5] ] },
    { "id": "M", "op": "+", "target": 6,  "cells": [ [5,1], [5,2] ] },
    { "id": "N", "op": "+", "target": 5,  "cells": [ [5,3], [5,4] ] }
  ]
}

Coordinates are 1-based: [row, col]. Every cell belongs to exactly one cage.

Policies (declarative JSON rules)

Controls

Color cages Probe uniqueness (second solution)

Puzzle Solution Summary

Uniqueness Probe

(toggle “Probe uniqueness” then Run)

Answer (newly derived facts)

computing…

Reason Why (mathematical English)

(click “Run ARC”)

Check 0

computing…