Arithmetic Cage Puzzle
Fill each row and column with the digits 1 through N exactly once. Every outlined connected cage must also reach its printed target using its displayed operation. For two-cell subtraction use the absolute difference; for division the larger digit divided by the smaller must be an exact integer. The generator checks that a puzzle has exactly one solution under bounded search. Clue-density tiers are not calibrated human difficulty grades.
Key features
- 4×4, 5×5 and 6×6 Latin rows and columns with connected arithmetic cages
- Addition and multiplication over 2–4 cells; subtraction and exact division over two cells
- Strict coverage, adjacency, operation and target validation for user-authored puzzle JSON
- Bounded two-solution search distinguishes unique, multiple, none and inconclusive limit
- Candidate-derived cell and row/column single-position hints without guessing
- Keyboard/touch entry, conflict highlighting, optional solution reveal, local JSON and puzzle-only SVG
How to use
- Choose the size, clue-density tier and allowed multi-cell operations, then generate or load the mixed-operation example.
- Read the target and operation in each outlined cage; use the text list below the board for exact coordinates.
- Enter 1–N with the keyboard or number buttons, moving with arrow keys and clearing with Delete.
- Check the grid or ask for a candidate-based logical hint; repair any highlighted conflicts.
- Save a session to local JSON, load it later, export a blank puzzle SVG or deliberately reveal the answer.
Use cases
- Practice exact division and arithmetic constraints in a small logic grid
- Compare how a cage target narrows the possible digits in a row and column
- Create an offline printable puzzle with a verified unique solution
Frequently asked questions
How do division and subtraction cages work?
Both have exactly two cells. Subtraction uses the absolute difference. Division takes the larger value over the smaller, and only an integer quotient is valid. A non-integer target cannot be accepted as a solution.
Do numbers in a cage have to be different?
Digits cannot repeat within the same row or column. Cells in a cage on different rows and columns may share a digit if the cage arithmetic allows it.
Are all cages connected and all cells covered?
Yes. Each cell belongs to one cage, and cells in each cage form an orthogonally connected region. Overlaps, gaps and diagonal-only connections are rejected on import.
Is a generated puzzle guaranteed unique?
Every returned puzzle passed a bounded search that looked for two distinct solutions. Generation may fail visibly if the total time limit prevents a sufficiently usable puzzle. The tier controls cage grouping only and does not certify human difficulty.
What do hints prove?
A cell hint means only one digit survives current row, column and cage-tuple constraints. A row or column hint means only one cell can hold that digit. If no such step exists, the tool says so; it does not reveal a guessed digit.
Does the tool upload my puzzle?
No. Solver, JSON import/export and SVG drawing run in the browser tab. The SVG has only cage targets and boundaries, never your entries or the revealed answer.
Privacy
Puzzle data remains in the current browser tab until you choose to download or load a local JSON/SVG file. The tool does not upload it.
Comments & questions