There are in general simple algorithms for determining S in polynomial time, since it’s just a system of linear equations as in the post. Humans came up with those algorithms, and smart LLMs may be able to recognize the problem type and apply a suitable algorithm in chain-of-thought (with some probability of success).
However, average humans don’t know any linear algebra and almost certainly won’t be able to solve more than a trivial-sized problem instance. Most struggle with the very much simpler “Lights Out” puzzle.
There are in general simple algorithms for determining S in polynomial time, since it’s just a system of linear equations as in the post. Humans came up with those algorithms, and smart LLMs may be able to recognize the problem type and apply a suitable algorithm in chain-of-thought (with some probability of success).
However, average humans don’t know any linear algebra and almost certainly won’t be able to solve more than a trivial-sized problem instance. Most struggle with the very much simpler “Lights Out” puzzle.