Free calcudoku puzzles, solver and printables

KenKen Rules and How to Solve

Learn the four rules with small examples, then solve a 4x4 puzzle one explained step at a time.

KenKen rules are simple: fill a square grid with the digits 1 to N so that each digit appears once in every row and column, and make each cage’s digits reach its target number with its operation. This page explains those rules with small examples and an interactive lesson that runs in your web browser. There is no sign-up, and nothing needs to be installed.

Puzzles are made on your device, and nothing is uploaded. Every puzzle has exactly one solution, because the built-in solver checks it before the puzzle is shown. Grids range from 3x3 to 9x9.

The same puzzle type is also called calcudoku, mathdoku or kendoku. This site uses the names “KenKen-style” and “calcudoku” for its puzzles. KenKen is a registered trademark of Nextoy, LLC. This site is not the official KenKen and is not affiliated with it.

How to use this KenKen rules lesson

  1. Open the rules part first. It has four cards: Rows and columns, Cages, Subtract and divide, and Digits can repeat. Each card has a small example drawing.
  2. Open Walk through to see a 4x4 puzzle solved step by step. Press Next step to move forward. The shaded cells are the ones involved in each step, and the reason for the step is explained.
  3. Open Try it to solve a small 4x4 puzzle yourself. Fill the grid with your digits.
  4. Press Check to test your answer.
  5. Press Hint if you get stuck.
  6. Press Another puzzle to get a new puzzle.
  7. Pick a technique in the technique list under Walk through to read what it means and whether this puzzle uses it.
  8. Open Print to get a one-page summary of the rules, with the example puzzle and its answer.

Each technique in the list below the walk-through has a one-line explanation, and the list says whether the example puzzle needs it. The Walk through and Try it parts use the same kinds of rules, so you can read the rules first and then practise. If you want a puzzle to print for paper solving, use the Print part rather than the screen.

What are the KenKen puzzle rules?

KenKen rules have two parts. First, fill an N x N grid with the digits 1 to N so that each digit appears once in every row and once in every column. This is a Latin square, like sudoku without the boxes. Second, the grid is split into cages, marked with heavy outlines. The digits in a cage must produce the target number in its top-left corner, using the operation shown, such as 12+ or 6×.

For example, a three-cell 6× cage can hold 1, 2 and 3, because 1 × 2 × 3 = 6. A single-cell cage shows just a number, and that digit goes straight into the cell.

Can numbers repeat in a KenKen cage?

Yes, but only when the repeated cells are in different rows and columns. An L-shaped 4+ cage of three cells can hold 1, 2, 1, because the two 1s sit in different rows and columns. Two cells in the same row can never hold the same digit, since each row needs every digit exactly once.

What order do subtraction and division go in?

Subtraction and division cages always have exactly two cells. The target is always the larger digit minus the smaller digit, or the larger digit divided by the smaller. A 3− cage can hold 4 and 1, because 4 − 1 = 3. A 2÷ cage can hold 4 and 2, because 4 ÷ 2 = 2. The order of the two cells does not matter, so you can write either digit in either cell.

How do you start a KenKen?

Start with the single-cell cages, because their digits are given. Then check the small cages with a clear answer. In a 4x4 grid, a two-cell 3+ cage can only be 1 and 2, and a two-cell 7+ cage can only be 3 and 4. In a 6x6 grid, a two-cell 2÷ cage can be 1 and 2, 2 and 4, or 3 and 6.

After that, use these methods in order of simplicity:

  • Only one digit fits: a cell has just one possible digit.
  • Only one place for a digit: a digit can go in only one cell of a row or column.
  • Cage combinations: list the digit sets that reach the target, then remove any that conflict with the grid.
  • Pairs, hidden pairs, and a digit forced onto a line: needed for harder puzzles.
  • Triples: needed for harder puzzles still.

The site rates difficulty by these steps, not by grid size. Easy puzzles need only single-cell cages, “only one digit fits”, “only one place for a digit” and cage combinations. Medium puzzles also need pairs or a digit forced onto a line. Hard puzzles need a triple or one round of trial and error. Expert puzzles need deeper trial and error.

Frequently asked questions

Is calcudoku the same as KenKen?

Calcudoku is another name for the same puzzle type. KenKen is a registered trademark of Nextoy, LLC, so this site uses the names “KenKen-style” and “calcudoku” for its puzzles.

Do KenKen-style puzzles have only one solution?

Yes. Every puzzle this site makes is checked by the built-in solver before it is shown, so it has exactly one solution.

Do I need to sign up or install anything?

No. The tool is free and runs in your web browser. Puzzles are made on your device, and nothing is uploaded.

Can I print the KenKen rules?

Yes. The Print part makes a one-page sheet with the four rules, the 4x4 example puzzle and its answer. Use Print / Save as PDF and choose Save as PDF in the print dialog to keep a file.

Is KenKen harder than sudoku?

Not necessarily. A 4x4 or 6x6 puzzle is usually quicker than a 9x9 sudoku, while 9x9 hard and expert puzzles take longer because the cages give fewer direct clues.

What should I do if I am stuck?

In Try it, press Hint for help, or press Check to test your answer. You can also open Walk through, where each step explains its reason.