Japan-U.S. Team Solves 120-Year-Old Puzzle

   Tokyo, March 10 (Jiji Press)--A team of the Japan Advanced Institute of Science and Technology (JAIST) and the U.S. Massachusetts Institute of Technology said Monday that it has solved a puzzle that remained unsolved for over 120 years.
   The puzzle is whether it is possible to divide an equilateral triangle into three parts and form a square with the parts without turning them over.
   British puzzle writer Henry Dudeney proposed this challenge in a newspaper in 1902. It was known that a square can be formed with four parts divided from such a triangle without flipping any pieces, but it remained unclear if this could be achieved with three or fewer parts.
   The research team, including assistant professor Tonan Kamata of JAIST, located in Nomi, Ishikawa Prefecture, central Japan, applied the concept of topology to classify patterns in which equilateral triangles and squares are divided into three parts.
   By analyzing the relationships between the sides and vertices of the figures, the team mathematically proved that there is "no solution" when the triangle is divided into three or fewer parts.

(2025/03/10-23:41)

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