How do you even get an LLM to try to solve one of these problems? When I ask it just comes back with the name of the problem and saying "it can't be done"

By making it think for 100+ pages https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925d... Regular ChatGPT users don’t have a way to do that, this is something they do internally only.

edit: apparently that’s only the _condensed summary_ of the chain of thought.

you can do this easily with the api or with codex

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Maybe you need to phrase it better. Like with a more specific direction of thinking.