Except the problem here is that you spoiled the solution. It is quite difficult to provide hints that don't spoil. Or rather, don't provide hints but rather tell it that it is wrong.

Here, I'll demonstrate it. First I'll prod it with vague responses about it just generally being wrong. Trying to leak no information to the model. We'll try to slowly add a bit more and then use your followups. Notice that the model cannot escape the overfit regime without your strong hints. You told the model specifically what to consider. You told it that it is a trick question of a trick question. This is not how a human would handle the situation. To my followups they wouldn't spit out the same answers. They'd actually likely followup with questions if they were confused. Which is a behavior I've never seen from an LLM: asking clarifying questions.

https://chat.openai.com/share/57ab9bca-326d-45cb-9257-7fb8c2...