Comment by keeda

Easily fixed by appending “Make sure to check your assumptions” to the question: https://news.ycombinator.com/item?id=42150769)

That’s the true power of these things. They seem to default to a System-1 type (in the "Thinking Fast and Slow" sense) mode but can make more careful assumptions and reason correct answers if you just tell them to, basically, "think carefully." Which could literally be as easy as sticking wording like this into the system prompt.

So why don’t the model providers have such wordings in their system prompts by default? Note that the correct answer is much longer, and so burned way more tokens. Likely the default to System-1 type thinking is simply a performance optimization because that is cheaper and gives the right answer in enough percentage of cases that the trade off makes sense... i.e. exactly why System-1 type thinking exists in humans.