It’s perhaps not obvious that in the example above, the LLM •does• actually do something useful! It conveys information about what’s typical: “When people talk about a goat and a boat and a river, there’s usually a cabbage too. Here are words that typically appear in the ‘answer’ position in such a context.”
What the LLM doesn’t do is actually solve the problem — or even understand the question in any meaningful way. Its answer is garbage. Garbage has clues, like a detective story. But garbage.