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In a classroom, one student (A) to another (B):

A: You wrote it on the board, right?

B1: I'm surprised! How did you know I wrote it.

B2: I'm surprised! How did you know I had written it.

What's the difference between B1 and B2?

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    Does this answer your question? Simple past vs Perfect Past
    – Lambie
    Commented Feb 18 at 19:25
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    There's no difference in meaning, and both are perfectly idiomatic. For most purposes, all you need to know is Simplest is best. But native Anglophones will sometimes choose to use the perfect in this exact context because they're particularly interested in what the addressee thought / knew at the time when they first encountered the "evidence". But that wouldn't usually be the case. Usually, the speaker doesn't particularly care about that level of "temporal precision" - all he wants to know is how the addressee came to his conclusion, whenever he did so.
    – FumbleFingers
    Commented Feb 18 at 19:40

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B1: I'm surprised! How did you know I wrote it?

B2: I'm surprised! How did you know I had written it?

The difference in meaning is in the wider context and not grammar here. If one thing precedes another and it is important or meaningful in a situation, we use the past perfect.

How did you know I had written it before you arrived? It was only when you arrived that you found out.

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