Japanese mathematics teacher and puzzle creator Tetsuya Miyamoto says he must have watched Bruce Lee's "Enter the Dragon" at least 20 times.
Miyamoto, whose numerical logical puzzle KenKen has achieved worldwide success over the past decade, was inspired as a teacher by the iconic scene in which Hong Kong-American actor Lee's character fools a bully who has picked a fight with him on a boat.
Antagonized with threats of violence and posed with the bully's question, "What's your style?" Lee responds, "My style? The Art of Fighting without Fighting."
Having thoroughly confused the bully, Lee points to an island where he says there will be more room to demonstrate.
Like the movie's protagonist, who makes the bully believe he will fight on the island but leaves him flailing alone in a sinking dinghy, Miyamoto sensei has developed his own unorthodox methodology to enlighten students: "The Art of Teaching without Teaching."
"It is a bare-handed method, using no tools" Miyamoto, 59, said in a recent interview in his arithmetic classroom located in Tokyo's Chiyoda Ward. "I thought of a style of teaching arithmetic to students where you 'win without fighting.' Without pushing, you get children to think, to become smarter."
Today KenKen, which Miyamoto invented in 2004 as an instruction-free method to help his third-grade students improve their calculation skills, appears in more than 150 newspapers worldwide, including The Times of London, the New York Times, Spiegel Online (Germany), and the Yomiuri Shimbun.
The puzzle, which in Japanese is called "kashikoku-naru-pazuru" (literally, puzzles that make you smarter), also trains your brain to think logically, Miyamoto says.
[Photo courtesy of Miyamoto Mathematics Classroom]
Last year marked the 25th anniversary of the Miyamoto Mathematics Classroom he started in Yokohama in 1993 on a first-come, first-served basis limited to just 20 students. He started teaching his first puzzles to third-graders in 1995. He currently teaches primary school students, grades 1-6.
"At the time there were puzzles for addition, puzzles for multiplication, but there were no puzzles that mixed all of it -- subtraction, addition, multiplication, division," he said.
KenKen, which basically means "cleverness squared," is a math-based symmetrical grid, ranging in size from 3-by-3 to 9-by-9. The goal is to fill the grid with digits, but none can appear more than once in any row or column. So, each row and column in a 4-by-4 grid would contain the numbers 1-4.
The grid also features heavily outlined groups of cells called "cages" and the top left corner of the cage contains a mathematical operation and "target" number. For example, a cage consisting of three cells with the sign +6 in a 4-by-4 puzzle must add together to equal 6. In this case, the numbers would be 1, 2, and 3.
KenKen puzzles that use only addition are the easiest but the puzzles get quite challenging when other arithmetic operations such as subtraction, multiplication and division are included in one puzzle.
More complex KenKen puzzles are formed using the same principles described above but excluding the signs for mathematical operations, thus making them another unknown for the puzzle solver to determine.
Miyamoto's puzzle creations feature interesting and intricate patterns in the final construction, something he says software such as the so-called "Kenerator" could never do.
"Automatic composition software could never create Mozart, it could never create Shakespeare. Machines don't have hearts," he said.
Unlike Sudoku, which doesn't require math but only logical thinking, KenKen is a puzzle that requires deeper thought, creativity and perseverance, Miyamoto says.
After Miyamoto made a number of TV appearances in Japan to speak about his puzzles, educational publisher Gakken Holdings Co., Ltd. released a kashikoku-naru-pazuru series in 2006, and many books were to follow.
The puzzles were unveiled overseas at the 2007 Bologna Book Fair. That same year, Gakken introduced them to toy inventor Robert Fuhrer, owner of Nextoy LLC, which has acquired the rights for KenKen outside Japan. Miyamoto did not have much say in the deal, he says.
Looking for a way to promote the puzzles, Fuhrer showed them to American puzzle creator Will Shortz, the crossword puzzle editor for the New York Times, and neighbor of Fuhrer's from Pleasantville, NY, who became thoroughly addicted to them, Miyamoto says.
"Will Shortz was hooked on the puzzles for like a month and said he would like to put them next to the New York Times crosswords. It was after that that the NY Times came to serialize them."
Meanwhile, chess international master David Levy had told Michael Harvey, an editor of the The Times (London), about the puzzles, and Harvey was impressed by their "depth and magnitude." The Times and NY Times started publishing the puzzles in 2008 and 2009, respectively.
Miyamoto, who graduated from Tokyo's prestigious Waseda University with a major in drama and literature even though he quit high school, says he hated school growing up because of teachers who barked orders, instead of allowing students to think on their own.
"Teachers give orders to students at schools but I rejected this way of thinking. You don't get smarter that way." He is dismissive of teaching methods that emphasize rote learning or memorization.
He worked for a cram school in Yokohama after graduation before he founded his mathematics class in 1993 and his unique methodology, "The Art of Teaching without Teaching," a practice he says cultivates a strong mind and heart through mathematics.
There are four types of mathematic problems, Miyamoto explained: easy and boring; easy and entertaining; difficult and boring; and difficult and entertaining.
"I only give students entertaining problems. The problems get tougher but whatever I give them they never give up," he said.
Miyamoto moved his class to Tokyo in 2009 and, after much success seeing his puzzles published worldwide, decided to transfer operations to "the center of the world" -- New York City's Manhattan, where he set up a classroom near Grand Central Station in April 2015.
By then, KenKen had already taken off, with annual international tournaments held in Westchester County, NY, since 2010, sponsored by the New York Times. But Miyamoto himself struggled to establish roots in the Big Apple.
After wedding through a Japanese marriage service, he decided to return to Japan to rekindle his business in March 2017. "I realized I could still grow in Japan. Growth and new challenges are always important for me. Now I am really enjoying myself," he said.
Among those new challenges will be fatherhood, when Miyamoto, who turns 60 in November, will celebrate with wife Wakaba, 41, the birth of their first child in March.
Miyamoto, who has authored over 180 books with more than 3 million copies sold worldwide, creates all his puzzles himself, so preparations take a painstakingly long time, he says. He believes KenKen fosters self-esteem in the puzzle solver and nurtures happiness using "the rules of mathematics that can be applied to life," like the patience required to climb a mountain and joy of reaching the summit.
"Happiness is about being yourself. Teachers can't teach you this. You have to find it on your own. Puzzles are a first step."
In 2018, Miyamoto started a new initiative, livestreaming classes via YouTube for second- and third-grade puzzle solvers who live too far away to travel to his lessons or are still on the waiting list -- puzzle classes remain limited to just 20 students.
On Dec. 24, 2018, he held his inaugural championship puzzle event at the Sugamo Gakuen school in Tokyo's Toshima Ward, limited to 30 students each in grades 1-5. There was a positive feedback from students and parents alike, according to Miyamoto's survey.
One feature of the final was the top three students in grades 3-5 had to create their own 6-by-6 puzzles with no mathematic operations in 20 minutes and have them tested for accuracy against analytical software. Students exchanged correct puzzles and solved them together, with the person who was able to successfully complete a puzzle first deemed the winner.
"I see myself as an arithmetic entertainer. I want to bring many more people into this classroom setting -- eventually even fill the Budokan or Tokyo Dome. I see the roadmap for Japan in entertainment education. Now it is about renewing my best record day by day."
You can check out Miyamoto sensei's classroom at http://www.miyamoto-mathematics.com/ and the KenKen website, as explained by Will Shortz, at https://www.kenkenpuzzle.com/