Puzzles

Yoshiaki Araki

President of the Japan Tessellation Design Association; 1996 Faculty of Environmental Information, 1998 Graduate School of Media and Governance Master's, 2001 Graduate School of Media and Governance Ph.D.

Imagine a jigsaw puzzle where the resulting picture is different every time. The pieces are simple in shape and pattern, and they are all identical.

Since 2014, our association has been holding "Math x Art" exploration events across Japan using this "T3 Puzzle." The pictures created by participants of all ages and genders vary widely, including their own names, seasonal foods, and everyday scenery. None of these are pre-prepared answers; they are works of art created by the participants themselves.

The appeal lies in encountering new works that exceed expectations at every event. By being creative with the combination of simple pieces, a diverse range of works can be produced. However, the number of combinations is vast, and it is not easy to draw a work exactly as intended. What is important is to observe the arrangements found by chance, liken them to something familiar, and take the time to build the work.

In these uncertain times, why not play with the T3 Puzzle as a hint for exploration to find your own answers?

Maki Nakasuji

Professor at Sophia University, Professor at Tohoku University, Ph.D. in Science, Mathematician; 1998 Faculty of Science and Technology, 2000 Faculty of Science and Technology Master's, 2003 Faculty of Science and Technology Ph.D.

Have you ever played with a Rubik's Cube?

A "Rubik's Cube" is a cube consisting of six different colored faces, made of parts divided into 9 squares (3x3) on each face. The way to play is simple. You just rotate the rows vertically or horizontally to return the scattered colored parts back to the original cube where each face has a uniform color. This is very difficult. And once you start, it's so fun you'll find yourself hooked.

There are countless guidebooks for this puzzle in the world, but why does moving it in this specific sequence move this part to that spot without disrupting the other arrangements? Trying to understand that mechanism can quickly lead to confusion. That is where "mathematics" becomes effective. By mathematically describing the procedures and arrangements of this puzzle, we can create specific solution algorithms. The mathematics used here is a theory called "Group Theory," a field that investigates the properties of objects—not limited to numbers—by focusing on their operational structures. Mathematics is involved even in conquering the cube.

Yuji Yamada

Assistant Professor, Brookdale Department of Geriatrics and Palliative Medicine, Icahn School of Medicine at Mount Sinai; 2008 School of Medicine

Crossword puzzles are often considered a form of entertainment that may improve cognitive function, but in reality, the scientific evidence for this is not definitive. Under the expectation of such possibilities, multiple studies have been conducted, suggesting an association with slower declines in memory and other cognitive functions. However, these studies have limitations and have not been able to prove a causal relationship stating that "doing puzzles caused the delay in cognitive decline."

There are many advertisements in the world for things like "brain training effective for dementia," but these are not faithful to science and are merely hypotheses lacking sufficient evidence. It is important to note that hypotheses are often wrong, and at present, there is no proof of a causal relationship showing that specific apps or games—not just puzzles—are effective in preventing dementia. With that understanding, rather than over-relying on one thing, it is important for dementia prevention to gradually focus on a wide range of healthy habits, such as regular exercise, social interaction, moderation in alcohol, quitting smoking, treating high blood pressure and diabetes, and caring for your eyes and ears.

Tomonori Hatano

Teacher at Keio Futsubu School (Boys Junior High School)

As a Japanese speaker, the meaning of the noun "puzzle" comes to mind first, but the English word "puzzle" was used as a verb first, and expressions like "puzzle out a mystery" or "I’m so puzzled" are still commonly used today. Looking through an etymological dictionary, the origin of "puzzle" seems related to "pose" (which has become a loanword in Japanese), but there are various theories and it is not clear. It is truly a "puzzling" word. Speaking of puzzles, in the activities of the Futsubu English Research Club, I play a game called Scrabble with the students. It is like a crossword puzzle where you arrange letter tiles on a board to create English words and compete for points. There are 100 letter tiles prepared for one game. High-frequency letters in English like E and A have about 10 tiles each but are worth only 1 point. On the other hand, low-frequency letters like Q and Z add 10 points each if used. If you make the word "PUZZLE," it should be 20 points for the two Zs, but since there are only two Z tiles in total, it usually cannot be made. Words containing Z are precious in English, a fact that junior high school students notice immediately. Incidentally, it seems that the Polish and Czech versions of Scrabble have more Z tiles and lower point values for them.