No pre-prompting, although I can't be sure it didn't use memories. "No tools" should theoretically have prevented it from looking up memories. FWIW, Grok and Gemini both failed in a similar way.

With Python, it was able to successfully solve it in 9 minutes: https://chatgpt.com/s/t_6a8350ecddfc81919328caf68de74861

The real pain point is that at work, I use Codex and I'm currently working on a project that involves debugging some polyline topology, very similar to the path following puzzle. The vision is completely useless here.

Your VLM idea sounds good. Theoretically, the inverse problem (generating an SVG of a pelican riding a bike) can also be solved with a VLM that plans out how to draw it, not unlike a human planning out a path for their hand to follow.