KenKen-Style Solver (Calcudoku / Mathdoku),
targets in, finished grid out.

Field guide

How the KenKen-Style Solver works.

A KenKen-style puzzle, also sold as Calcudoku or Mathdoku, mixes Latin-square logic with arithmetic. The grid is n×n, and you place the digits 1 to n so that each appears exactly once in every row and every column, as in Sudoku but without the boxes. Heavy outlines split the grid into cages. Each cage shows a target number and an operator, and the digits inside it must reach the target when combined with that operator. A cage of a single cell shows just a number, which is the digit that goes there.

The four operations

Addition and multiplication cages can have any number of cells. In the standard rules, subtraction and division cages have exactly two, so the order of the digits does not matter. One detail trips people up: a digit may repeat inside a cage as long as its cells share no row or column. A bent cage of three cells adding to 4 can hold 2, 1 and 1, because the two ones sit in different rows and columns.

Entering your puzzle

Pick the grid size first. Then tap every cell of one cage, choose the operator, type the number printed in its corner and press Add cage. A tint separates neighbouring cages, and tapping a finished cage lets you change its target or delete it. The tool rejects targets that no digits can make, such as 7÷ in a 6×6 grid, and it warns when the selected cells do not touch. The Example button loads a practice puzzle written for this tool.

Using the cage helper

Every cage is a small puzzle on its own. In a 6×6 grid, 12× over two cells can only be 2 × 6 or 3 × 4, because 12 is too large for the other pairs. Over three cells it can be 1 × 2 × 6, 1 × 3 × 4 or 2 × 2 × 3, and the repeated 2 works only in a bent cage. The helper below the board lists these sets for any size, cell count, operator and target, so you can see what a cage allows before you place a digit.

What happens when you press Solve

The solver first lists every digit combination each cage allows, including the row and column rule between its own cells. It then keeps a list of possible digits for every cell and repeatedly removes any digit that no allowed combination supports. Digits already placed leave the rest of their row and column, and a digit that fits only one cell in a row is placed there. When that stops making progress it guesses in the most constrained cell and backtracks if the guess fails. A search limit keeps the page responsive, and after finding a grid the solver looks for a second one, so it can tell you when a puzzle is not unique.

Tips for solving by hand

• Start with the givens. One-cell cages fix a digit immediately and clear it from its row and column.
• Use the factors. In a 6×6 grid only the digit 5 is a multiple of 5, so a cage with a target divisible by 5 must contain it.
• Know the line total. Every row and column adds up to n × (n + 1) ÷ 2, which is 21 in a 6×6 grid. That is handy for finding a missing cage.

Disclaimer: This tool is an independent fan creation and is not affiliated with, authorized, or endorsed by Nextoy, LLC. “KenKen” is a registered trademark of its owner, and the name is used here only to describe the type of puzzle the tool solves. Calcudoku and Mathdoku are other names for the same style. Provided for practice and entertainment only; check the result against your own puzzle.