This project contains a complete proof of the isomorphism of the symmetry group of the 12-puzzle and the full symmetric group S_12.
The puzzle consists of 3 intersection circles and 12 beads. One is interested in moving the circles while the coloring configuration changes. The challenge is to swap colors (two-color version) or more complicated cases.
This paper was written fully with GPT 5 Pro and under my supervision. The current version was reiterated 6 times by GPT 5 Pro. The complete LaTeX file was automatically generated in GPT 5 Pro.
The second part is Streamlit code with visualization app. This app contains autosolver for the puzzle. The whole code was generated by GPT 5 Pro based on the paper.
The latex file was created via the prompt to GPT 5 Pro
https://chatgpt.com/share/68b3a2ce-7200-8007-b84d-bf70fbcd8a18
The prompt contains a link to my old blog. This problem has been solved by me before but the solution was never published. This is a genuinely new proof by GPT 5 Pro.
The Streamlit app was generated from a paper draft (+ minor modifications before the final effect)
https://chatgpt.com/share/68b3a32c-0db0-8007-b81c-1e47bb0667d1
To run the Streamlit app use
pip install streamlit matplotlib streamlit run puzzle.py
The paper went into a series of self-improving prompts which were reiterated up to version 7. I have read the version 7 to verify it.
https://chatgpt.com/share/68b3a371-b674-8007-bbc8-76de7ab9cfdb