[LINK] o/t: Sudoku .. now KenKen

[stephen at melbpc.org.au]

A New Puzzle Challenges Math Skills 

By WILL SHORTZ www.nytimes.com Published: February 8, 2009 


KenKen, which starts in The New York Times today next to the crossword 
puzzle, is a new numerical logic puzzle from Japan. 

The name means, "cleverness squared." 

(Play KenKen Online » http://www.nytimes.com/ref/crosswords/kenken.html)

KenKen shares some properties with sudoku. Each is a pure logic challenge 
in which numbers are filled in the squares of a grid. Unlike sudoku, 
though, in which the numbers act solely as symbols (letters or pictures 
would work as well), KenKen requires arithmetic.

The rules are simple: Fill the grid with digits so as not to repeat a 
digit within any row or column, and so the digits within each heavily 
outlined box (called a cage) go together using the arithmetic operation 
shown to make the target number indicated.

Two new KenKen puzzles will be presented in The Times each day from 
Monday through Saturday. The first is a four-by-four-square puzzle that 
increases in difficulty from easy to medium as the week progresses. The 
second is a six-by-six-square puzzle that goes from medium to hard.

KenKen was invented in 2004 by the Japanese educator Tetsuya Miyamoto, 
who founded and teaches at the Miyamoto Math Classroom in Tokyo. Students 
attend his class on weekends to improve their math and thinking skills. 

Mr. Miyamoto said he believes in “the art of teaching without teaching.” 

He provides the tools for students to learn at their own pace using their 
own trial-and-error methods. If these tools are engaging enough, he said, 
students are more motivated and learn better than they would through 
formal instruction.

About 90 minutes of class time each week is set aside for solving 
puzzles, usually designed by Mr. Miyamoto. 

The most popular one has been KenKen.

Given Mr. Miyamoto’s philosophy of not instructing, one hesitates to 
offer advice for solving KenKen, but here are some starting tips:

¶ Fill in any single-square cages immediately.

¶ Look for cages whose target numbers are unusually high or low for their 
number of squares. Often these have unique answers. For example, in a six-
by-six puzzle, two squares with a sum of 11 must be filled with 5 and 6, 
in some order. Three squares with a product of 10 must be 1, 2 and 5. 

¶ Remember that cages can repeat numbers, as long as the numbers do not 
appear in the same row or column. For example, a three-square L-shaped 
piece with a sum of 6 could be filled with 1, 2 and 3 or 1, 1 and 4 (with 
the 4 in the middle square of the L).

¶ Note that the order of the numbers in cages with subtraction and 
division doesn’t matter. 

¶ Don’t forget that each row and column must contain every digit. When 
you have exhausted arithmetic, use sudoku logic.

And now you’re on your own.

--
Cheers,
Stephen


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