You should never answer, "Yes, I know how to solve this." That's almost never true. Even if you ask me to recreate code I wrote before, I can't for sure know I'll do it the exact same way, or not encounter difficulties.
A truthful answer can be, "I believe I can solve this."
The ability to explain what you're doing is critical. But I don't think it's tied to having an answer memorized or not.
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