There Are Magic Hexagons of Every Order

190 points · 31 comments on HN · read original →

Points and comments are a snapshot, not live.

Magic hexagons exist for all orders greater than 2 using a new parameterized construction.

The article presents a construction for magic hexagons of every order (except order 2). By introducing a starting index parameter and using a potential field abstraction, the author proves that solutions exist for all orders n > 2. The construction relies on Langford sequences and is formalized with the help of LLM-based proof assistants. Interactive visualizations demonstrate the potential field symmetry.

What commenters are saying

Commenters praised the interactive elements and the potential field concept. One noted the order-2 impossibility due to forced equal numbers. Another clarified that the consecutive constraint is unusual; typical magic squares only forbid duplicates. A commenter critiqued the LLM proof discussion as distracting. Others linked related contests and noted the 'hexagon is bestagon' meme.