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Tutorial (Beginner)

Beginners Tutorial

New to KENKEN? Don’t be scared. There are some simple techniques that will help you solve the easier puzzles. Let’s learn them as we walk through solving a 3 x 3 grid, step-by-step.

Now are you ready for a 3x3?

Here’s our sample grid: 3 columns and 3 rows.

Every square in this grid will contain one of the numbers 1, 2, or 3. A number cannot be repeated within any row or column.

The heavily-outlined areas are called “cages.” The small number in the upper-left corner of each cage is our “target number.” The math symbol next to the target number tells us which operation we’ll be using in that cage. This puzzle uses only addition.

Cages that are around only one square are the easiest to solve. The target number is the number that goes in the square.

OK, those are the basics. Now let’s clear the grid and start filling it in, step-by-step.

The top-right corner is a single-square cage with a target number of 1. So we know we can only put 1 in there.

See the cage we’ve highlighted in red? It’s two squares with a target number of 3, and we’re using addition. So the only combination of two numbers between 1 and 3 that will add up to our target number (3) is… 1 and 2. But which square gets the 1 and which gets the 2?

Our top row already has a 1 in it (top-right square). So the top-left square, which is in the same row, can only have the 2 in it. Which means the 1 will go in the square below it.

Each column in a 3 x 3 grid must have the numbers 1, 2, and 3 in it. The far-left column already has a 1 and 2 in it, so 3 must go in the bottom-left square.

Now let’s complete that cage. The target number is 4, and 3 + 1 = 4, so 1 must go in the bottom-center square.

Each row in a 3 x 3 grid must also have the numbers 1, 2, and 3 in it. So the bottom-right square must contain a 2.

We’ve highlighted another two-square cage in red. Target number is 5, we already filled in a 2, and we know 2 + 3 = 5. So we fill in a 3 in the other square.

With the same logic (using addition, or just knowing which numbers need to be in every row and column), we can fill in the remaining two squares.

And... voilà! Puzzle completed! Although there is only one solution to every KENKEN puzzle, there are many different paths to that solution. Try this grid a few more times, each time starting with a different cage.


Now, try and try a sample puzzle!

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Welcome to KENKEN!

No matter what you're looking for — learning or fun — KenKen.com has it! Free online puzzles. Cool math games. Number games. (More addictive than Sudoku or Kakuro? You decide!) Educational games for kids. Visit our For Teachers section for math teacher resources, our free KenKen Classroom program, and a message from Tetsuya Miyamoto, the Japanese educator behind KenKen. Miyamoto, chess master David Levy, and the rest of Team KenKen have crafted these math puzzles into great games for learning and brain training. Need even more KenKen? Check out our Will Shortz Presents books. Try our mobile app on iPhone and iPad or our Kindle version. Play on the New York Times puzzle page and NCTM website. Regardless of why, how, or where you play, KenKen are the math puzzles that make you smarter!

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Team KenKen