I am... unsure why anyone would think LLMs would be able to do this. They are not magic oracles. Like I think even most humans would be extremely bad at this. Like, are people actually using LLMs for this? Please do not, it won't work.
But nothing prevents llms from being RLed to do this right? But does training llms to be better at this, improves their world model or does it only make changes at the surface?
The problem itself is unsolvable given the data provided.
You could conceivable make it better at making guesses, but they will inherently always be guesses that will sometimes be wildly off.