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Is KenKen the next Sudoku?

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Cross with crosswords? Sick of Sudoku? Say hello to your next airplane addiction.

It's called “KenKen” -- Japanese for “wisdom squared” -- and it’s the smartest pencil-and-paper puzzler since Sudoku itself. It even promises to sharpen up your math skills.

Created in 2004 by Japanese math teacher Tetsuya Miyamoto, KenKen was popularized in the United States by New York Times crossword puzzle editor Will Shortz, who was introduced to the game when agent and toy industry legend Bob Fuhrer called and asked him to try out a new puzzle.

“I say no to most requests like this,” Shortz told Yahoo! Games, “simply for lack of time. But Bob lives in the town next to mine, and he promised to take no more than 5-10 minutes, so I said OK.”

It would turn out to be the start of a serious habit -- not just for Shortz, but for thousands of Americans.

“Bob came to my house. Briefly explained KenKen. I tried one. Then I tried another. Then I tried a third one. Then I asked him to leave a Japanese KenKen book with me...which I proceeded to devour during the following week. I was completely hooked.”

A few years later Shortz began including KenKen puzzles in the New York Times, first in the daily paper, and later in Sunday’s magazine.

“It appeals to a different sort of solver from the typical crossword doer,” he said, “so I thought it would make a nice complement to the Times' famous crossword.”

You’ll probably note that it looks a lot like Sudoku, and it does. And it plays a lot like Sudoku, too. The basic rules are the same: numbers appear once (and once only) in every horizontal row and vertical column of the grid. But whereas Sudoku is a game of pure logic, KenKen puts the numbers to work.

Instead of Sodoku’s three-by-three squares, KenKen’s puzzles are divided into irregular “cages,” each marked with a target number and a mathematical operation -- add, subtract, multiply, divide. You have to fill in the cage so that the numbers, when combined with the operation, equal the target.

Say you have a two-number cage saying “5+,” for example. You need to fill in the numbers so that when used with the mathematical operation, they give the target number. In this case, here “2” and “3” would be one possibility, and “1” and “4” would be another. The only other, in fact. That’s a simple example -- big cages could span four or more squares, growing the complexity exponentially.

And that’s one of the puzzle’s greatest strengths: its predictable difficulty level. Smaller KenKen puzzles are really simple. Three-by-three puzzles are easy enough for a reasonably bright second-grader, making the game popular with many elementary school teachers as a way to add some pep to math classes.

But the larger, harder ones (they go all the way up to nine-by-nine) will make even the most experienced puzzlers sweat, stretching out both logic and mathematics skills to their limits. Quick: which numbers can be multiplied together to give 160? Play enough KenKen and you’ll be surprised at just how quickly you’re able to answer that question.

So where to get started? Right here, with this online version of the game, and these helpful hints.

-- Use a pencil. Sudoku fans will know this one already. You’ll often want to jot down possible numbers in the corner of the boxes, and replace them with the correct one later on. Having a pencil and an eraser on hand is all but essential.

-- Look for cages containing just one number. No prizes for guessing what goes in there -- and no prizes for guessing why nailing these down is job-one for solving any KenKen grid.

-- Look for cages that only have one possible solution. A two-square cage reading “3+,” for instance. Only 1 and 2 can go in those boxes -- there’s no other possible combination.

-- Numbers can be repeated. Unlike Sudoku, where the three-by-three boxes can only contain each number once, appropriately shaped KenKen cages can hold repeated numbers. A three-cell KenKen cage marked with a “7+,” say, could contain two 3s and a 1, if it was an L-shape, and the 1 needs to go in the corner of the L.

-- Never, ever guess. The golden rule. A properly made KenKen grid doesn’t need any guesswork. Try it and you’re likely to send yourself off down a dead end, turning your grid into an unsolvable mess. If you run out of definite answers, you’ve missed something somewhere -- or made a mistake.

Hungry for more KenKen? You’ll find them printed in the New York Times (most helpfully on the paper’s web site, which has a handy Flash version offering a variety of difficulty levels) as well as about a hundred other daily newspapers. iPhone and Android apps are available, too, though if you really are looking for something to keep your mind humming on your next flight, you’re best off with one of Shortz’s many KenKen books. You won’t have to put them away when it’s time to land.

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