This is the way I think about it.

I = E / K

where I is the intelligence of the system, E is the effectiveness of the system, and K is the prior knowledge.

For example, a math problem is given to two students, each solving the problem with the same effectiveness (both get the correct answer in the same amount of time). However, student A happens to have more prior knowledge of math than student B. In this case, the intelligence of B is greater than the intelligence of A, even though they have the same effectiveness. B was able to "figure out" the math, without using any of the "tricks" that A already knew.

Now back to your question of whether or not prior knowledge is required. As K approaches 0, intelligence approaches infinity. But when K=0, intelligence is undefined. Tada! I think that answers your question.

Most LLM benchmarks simply measure effectiveness, not intelligence. I conceptualize LLMs as a person with a photographic memory and a low IQ of 85, who was given 100 billion years to learn everything humans have ever created.

IK = E

low intelligence * vast knowledge = reasonable effectiveness