KenKen - Math Cage Logic Puzzle

KenKen is a captivating number puzzle that combines the row-and-column uniqueness of Sudoku with the arithmetic challenge of math cage constraints. Every puzzle is a grid of cells grouped into “cages”, each labelled with a target number and an operator. Your mission: place the right digits so that every cage computes correctly and every row and column holds each number exactly once. Simple to learn, deeply satisfying to solve!

The Objective

Fill the grid with digits so that each row and each column contains every number from 1 to the grid size exactly once, and the values in each cage combine — using the cage’s operator — to hit the cage’s target.

The Tools You Have

You get a choice of 4×4, 5×5, or 6×6 grids, selectable from the dropdown in the header. Each cell belongs to a cage outlined with bold borders. The top-left cell of each cage shows its target number and operator (e.g., 6*, 5+, 2/). A number keypad at the bottom lets you tap digits into the selected cell. The pencil (Notes) button in the header lets you jot candidate numbers inside a cell without committing to an answer. The Eraser button clears the selected cell, and the New Game button generates a fresh puzzle.

The Rules to Follow

1. Digit range: Use digits 1 through N in an N×N grid (1–4 in 4×4, 1–5 in 5×5, 1–6 in 6×6).
2. No repeats in rows or columns: Each digit must appear exactly once in every row and exactly once in every column.
3. Cage arithmetic: The numbers placed in a cage must produce the cage’s target when combined with its operator:
   • + — the numbers sum to the target.
   • − — the larger number minus the smaller equals the target (two-cell cages only).
   • × — the numbers multiply to the target.
   • ÷ — the larger number divided by the smaller equals the target (two-cell cages only).
   • No operator — the single cell must equal the target exactly.
4. Conflicts are highlighted: Any row or column with a repeated digit turns red so you can spot the mistake immediately.
5. Error cages: If a completed cage does not satisfy its constraint, its bold border turns red.

Simple Strategy

Start with single-cell cages — they tell you the exact digit for that cell. Then look for two-cell division cages, since exact integer division strongly limits the possible pairs. Cross-reference the known values against the row and column restrictions to eliminate candidates quickly.

Example of Play

In a 4×4 grid, suppose you see a cage 6* covering three cells in the top row. The only way to multiply three distinct digits from {1,2,3,4} to get 6 is 1×2×3. You also know from column constraints which of those cells gets which value. A neighbouring single-cell cage 4 locks one column position immediately, which then resolves the remaining ambiguity in the multiplication cage.

Tips for Beginners

• Single-cell cages first: they give you free digits that cascade into neighbouring constraints.
• Division cages are highly restrictive: in a 4×4 grid a 2/ cage can only be {1,2} or {2,4} — use that to anchor entire rows.
• Use Notes mode: pencil in all candidates for a cell, then eliminate them one by one as rows and columns fill up.
• Watch the cage borders: a red border means the cage total is wrong even if no row/column conflict is flagged yet.
• Larger grids, same logic: 5×5 and 6×6 introduce more candidates per cage, but the row/column uniqueness rule stays as powerful — let it do the heavy lifting.