KenKen Puzzle Generator
Fresh arithmetic grid puzzles from 3×3 to 7×7. Every one is solved before you see it and thrown away unless the answer is unique.
KenKen puzzle
Click a square and type a number. Arrow keys move, Backspace clears.
The rules
- Every row and every column holds each number from 1 to the grid size exactly once.
- The heavy outlines are cages. The small label is a target and an operation.
- The numbers in a cage must combine to make the target using that operation.
- Numbers may repeat inside a cage, as long as they do not repeat in a row or a column.
- A cage of one cell is simply that number.
Solving, and how these are made
- Start with the single cells and the extreme cages. A cage of two making a large product, or a difference equal to the grid size minus one, usually has only one pair that fits.
- Numbers may repeat within a cage. This is the rule people get wrong most often — the only restriction is rows and columns, so a three-cell L-shaped cage can hold two of the same number if they are not in line.
- A difference or division cage does not tell you which cell is larger. It cannot: the clue would be different depending on which way round you read it, and the solver has no way to know. That is also why those only ever appear on two cells.
- Every puzzle here is solved before you see it and thrown away unless the answer is unique. A generator that skips that step makes puzzles with several answers — they look fine, and a careful solver who finds a different valid grid is told they are wrong.
- Bigger cages are not automatically harder. A four-cell sum often pins less than a two-cell difference, which is why the harder labels are used more often.
How to use
- Pick a grid size and how big the cages may get.
- Click a square and type a number — arrow keys move.
- Press Check at any point, or Print for a paper copy.
Frequently asked questions
Can a number repeat inside a cage?
Yes, and this is the rule people get wrong most often. The only restriction is that each number appears once per row and once per column. An L-shaped cage of three cells can hold two of the same number, as long as those two are not in the same line.
Which cell of a subtraction cage is the bigger one?
The clue does not say, and it cannot. If it did, the same cage would need a different label depending on which way round you read it, and you have no way to know. So the target is the difference either way — and that is also why subtraction and division only ever appear on two-cell cages, since with three the answer would depend on an order nobody can see.
Could a puzzle have more than one answer?
No. Each one is solved before it is offered and discarded unless exactly one grid fits. Generators that skip this produce puzzles that look perfectly fine, and a careful solver who reaches a different valid grid is told they are wrong.
Where should I start?
Single-cell cages, then the extreme ones — a two-cell cage with a large product, or a difference equal to the grid size minus one, usually has only one pair that can make it. Big cages are not automatically harder; a four-cell sum often pins less than a two-cell difference.
What does the cage size setting change?
The largest blob the grid is cut into. Smaller cages give more clues per square and an easier puzzle; larger ones give fewer, looser constraints. It does not change the size of the grid or the numbers used.
Is this the same as Killer Sudoku?
They are cousins. Killer Sudoku is a sudoku grid with sum-only cages and the usual 3×3 boxes; this is a plain Latin square with cages that use all four operations and no boxes. The cage rules here are simpler, and the arithmetic does more of the work.
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