What Is KenKen? A Beginner's Guide to the Sudoku-Meets-Math Puzzle

If you love Sudoku but wish it had a little more to chew on, KenKen is your next obsession. Invented by a Japanese math teacher to make arithmetic fun, it blends the row-and-column logic of Sudoku with light mental math. Don't worry — the math never gets harder than your times tables, and the puzzle does all the bookkeeping. Here's everything a first-timer needs to start solving.

The two rules of KenKen

A KenKen is a square grid — 4×4, 5×5 or 6×6 to start. There are only two rules, and the first will feel familiar:

• Latin square rule: fill each row and each column with the numbers 1 up to the grid size, using each number exactly once — no repeats in any row or column, just like Sudoku.
• Cage rule: the grid is divided into heavily-outlined blocks called 'cages'. Each cage shows a small target number and a math symbol. The numbers you write in that cage must combine, using that operation, to make the target.

Reading the cages

The little label in the corner of each cage tells you everything. The symbol is the operation:

• × — the numbers in the cage multiply together to the target. '12×' over two cells could be 3 and 4.
• + — the numbers add up to the target. '7+' over three cells could be 1, 2 and 4.
• − — the (two) numbers subtract to the target. '2−' could be 5 and 3, or 3 and 1.
• ÷ — the (two) numbers divide to the target. '3÷' could be 6 and 2, or 3 and 1.
• A cage with just a number and no symbol is a freebie: write that number straight in.

How to solve it, step by step

Beginners often stare at the whole grid and freeze. Don't — KenKen is solved one small deduction at a time. Here's the reliable order of attack:

• Fill the freebies first. Every single-cell cage is a gift and often unlocks its row and column.
• Hunt for cages with only one possibility. On a 4×4, a '12×' two-cell cage must be 3 and 4 — you may not know the order yet, but you've narrowed it to two cells.
• Use the no-repeat rule to fix the order. If one of those cells is in a row that already has a 4, the 4 must go in the other cell.
• Pencil in candidates. When a cage has a few options, jot the possible numbers small in the corner, then eliminate them as rows and columns fill.
• Work the tight rows. A row missing just two numbers, crossed by a cage, usually collapses to a single answer.

A quick worked example

Picture a 4×4 with a '2÷' cage covering two side-by-side cells in the top row. Divisible pairs from 1–4 are (1,2), (2,4) — and (2,1),(4,2). Now suppose the column under the left cell already contains a 2. That rules the 2 out of the left cell, so the pair must be 4 and 2 with the 4 on the left. One cage, two cells solved — and those numbers now trim the possibilities everywhere they touch. That cascade is the whole game.

Tips that make it click

• Start with the smallest cages — fewer cells mean fewer combinations to consider.
• Remember subtraction and division cages are always exactly two cells, so they have very few options.
• For a '+' or '×' cage, the target's factors or sums quickly reveal which numbers can even fit.
• If you get stuck, count what's missing from a nearly-full row or column instead of staring at cages.
• Every well-made KenKen has exactly one solution, so you never have to guess — there's always a logical next step.

Try one now

The best way to learn is to solve a gentle one. Our free KenKen generator makes 4×4 puzzles perfect for beginners, then 5×5 and 6×6 when you're ready to level up. Every puzzle is guaranteed to have a single solution, and you can play in your browser or print a clean PDF with the answer key. Start small, trust the logic, and you'll be hooked by your second grid.