KenKen / Calcudoku Solver

Draw the cages of a KenKen or Calcudoku from a book or app, enter each target and operation, and the tool checks that the puzzle has exactly one answer, shows the solution, or reveals one cell at a time with the rule behind it.

How to use

1. Choose the "Size" (3×3 to 9×9). To try the tool first, press "Example 4×4" or "Example 6×6".
2. In "Cages" mode tap the cells of one cage, type the target on the keypad, pick the operation (+ − × ÷, or "none" for a one-cell cage) and press "Make cage". The cage gets a thick outline and its label in the top-left cell. "Unpick" cancels the selection and "Delete cage" removes the cage under the selected cell.
3. If the puzzle shows some digits, switch to "Digits" mode and enter them. The message under the grid names cells without a cage, cages that overlap, − or ÷ cages that do not have two cells and targets that cannot be reached.
4. Press "Solve". The answer appears in blue with a message saying whether it is unique. "Hide answer" removes it, and "Hint: one cell" fills one cell in green and explains why.
5. "Save as PNG" downloads the grid as shown. "Clear all" empties the board.

How it works

• For every cage the solver lists the digit combinations that still fit the target and the row and column rule, keeps only the digits that appear in them, and tries values when the rules stall. It also uses the fact that every row and column adds up to 1 + 2 + … + N. It keeps searching after the first answer to check uniqueness and stops after 10 seconds.
• Hints look for, in order: a one-cell cage, a cell whose row and column already hold every other digit, a digit with only one place in a row or column, and a cage whose combinations leave one digit for a cell. Otherwise one cell comes from the solution and the message says so.
• The board, the answer and the hints are kept in this browser only.

KenKen and Calcudoku rules

An N×N grid holds the digits 1 to N once in every row and every column; there are no boxes. The grid is divided into cages. The digits of a cage must give its target with its operation: added, multiplied, or for a two-cell cage, the larger minus the smaller or the larger divided by the smaller. A one-cell cage simply holds its number. A digit may repeat inside a cage if the cells are in different rows and columns.

Solving KenKen by hand

Write in the one-cell cages first. Then look for cages with few possibilities: in a 6×6, a two-cell 11+ can only be 5 and 6, a 2÷ can be 1 2, 2 4 or 3 6, and a 5− can only be 1 and 6. Products help as well: a two-cell 30× in a 6×6 must be 5 and 6.

When two cages in the same row are reduced to the same pair of digits, those digits leave the rest of the row. Near the end, use the row sum: a row of a 6×6 adds up to 21, so a missing digit is 21 minus the others.

Questions and answers

What if the solver finds more than one answer?

A well-made KenKen has one answer, so several answers usually mean a cage is missing, a target or operation was misread, or a cage has the wrong shape. One possible answer is shown so that you can compare it with the paper.

Is Calcudoku the same as KenKen?

Yes, Calcudoku and MathDoku use the same rules: a Latin square with arithmetic cages. Some versions hide the operation; this tool needs the operation of each cage.

How does a − or ÷ cage work?

It always has two cells. Subtract the smaller digit from the larger, or divide the larger by the smaller, so the order of the cells does not matter. 3− in a 6×6 can be 1 4, 2 5 or 3 6.

Which sizes are supported?

3×3 to 9×9. Larger grids with many big + or × cages take longer; the search stops after 10 seconds.