Puzzles

2024/03/27

Yoshiaki Araki

President of 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" inquiry 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 exactly what you intend. What is important is to observe the arrangements you find by chance, liken them to something familiar, and carefully build your work.

In these unpredictable times, why not try playing with the T3 Puzzle as a hint for inquiry 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 a 3x3 grid of nine squares on each face. The way to play is simple. You just rotate the rows vertically or horizontally to return the cube to its original state where each face is a solid 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 a certain sequence move a specific part to a specific spot without disrupting the other arrangements? Trying to understand that mechanism can quickly lead to confusion. That is where "mathematics" becomes effective. By describing the procedures and arrangements of this puzzle mathematically, we can create specific solution algorithms. The math 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 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—that "doing puzzles caused the delay in cognitive decline."

There are many advertisements 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, let alone puzzles, are effective in preventing dementia. With this understanding, rather than over-relying on one thing, it is important for dementia prevention to gradually mind 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 noun meaning of "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 is also a loanword in Japanese), but there are various theories and it is unclear. It is truly a "puzzling" word. Speaking of puzzles, in the activities of the Futsubu English Research Society, I play a game called Scrabble with the students. It is like a crossword puzzle where you compete for points by arranging letter tiles on a board to create English words. There are 100 letter tiles provided for one game. Letters like E and A, which appear frequently in English words, 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 were to 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, I hear that the Polish and Czech versions of Scrabble have more Z tiles and lower point values for them.