There are certainly emergent capabilities that come out of the training process of being able to predict next tokens, and it's shown that LLMs often can solve logic and math problems, riddles, etc. which are not in it's training data because deep in the internal layers of the model it has something resembling logic and reasoning abilities. This can be seen in the "benchmark" results of papers like the GPT-3 and InstructGPT papers, among many others, where they tried pretty hard to test the models against questions which were not part of the training.
This is also shown in the Codex paper, where they trained an LLM to write code and then watched it solve a number of code problems they handwrote originally to make sure the problems could not have been in the training data.
Try it out yourself, make up some little math word problems and ask chatGPT or something.
Of course, advent of code will be much more challenging problems, but to get help with some subcomponents of the problem a motivated participant would likely try to use the most recent, powerful, and advanced models which outperform the results from papers written a few years ago, and outperform the free chatGPT.
This is also shown in the Codex paper, where they trained an LLM to write code and then watched it solve a number of code problems they handwrote originally to make sure the problems could not have been in the training data.
Try it out yourself, make up some little math word problems and ask chatGPT or something.
Of course, advent of code will be much more challenging problems, but to get help with some subcomponents of the problem a motivated participant would likely try to use the most recent, powerful, and advanced models which outperform the results from papers written a few years ago, and outperform the free chatGPT.