I'd still ask for the definition of factorial.

Sure, for various reasons, most programmers know the factorial, but I'd consider remembering the definition of some mathematical operation only common in certain domains (statistics and finance?), that most people only learn in high school and never use again, to be rote memorization.

Ability to detect your deficiencies of knowledge and ask questions is hugely important, and is worth testing.

Or you can use a search engine.

Not particularly factorial problem, but the general interview questions require some amount of prior knowledge about the techniques. Topics like math based or bit manipulation, permutations/combinations have questions which are often asked in Interviews and require some prior knowledge to be able to give optimized solutions.

Also if it's legitimately the first time you're solving something like "all permutations" you'll be slower than someone who has done it before, and that might hurt you too.