Learn Hardcore French: Vous auriez trouvé le drap si personne n’avait déplacé l’armoire. - You would have found the sheet if nobody had moved the wardrobe.

It’s the conditional perfect (conditionnel passé): conditional of the auxiliary (auriez) + past participle (trouvé). It expresses a past hypothetical result that didn’t happen. Pattern: si + plus-que-parfait → conditionnel passé.

What tense is n’avait déplacé in the si-clause, and what’s the rule?

It’s the plus-que-parfait (imperfect of the auxiliary + past participle). In counterfactual past conditions, French uses:

si + plus-que-parfait (condition) → conditionnel passé (result) Example here: si personne n’avait déplacé… → vous auriez trouvé…

Why not say si personne n’aurait déplacé l’armoire?

In standard French you never use the conditional after si to state a condition. Use the indicative (here, plus-que-parfait): si personne n’avait déplacé… Colloquial speech may sometimes produce this, but it’s considered incorrect.

How does personne work here? Do we need ne? Should we add pas?

Personne is a negative pronoun meaning “no one.”
As subject, the structure is Personne n’ + verb. After si, it stays the same: si personne n’avait déplacé…
Do not add pas: personne already negates the verb. Personne n’avait pas… is wrong or at best changes the meaning.
In careful writing, keep ne. In very casual speech, people may avoid it by rephrasing (e.g., Y a personne qui a déplacé…), but not in this sentence’s formal style.

Why isn’t there agreement on trouvé? Should it be trouvée?

With avoir, the past participle agrees only with a preceding direct object. Here, the object le drap comes after the verb, so no agreement: trouvé.

If the object came before as a pronoun and were feminine: Vous l’auriez trouvée (e.g., referring to la couverture).
Plural object pronoun: Vous les auriez trouvés/trouvées.

Can I put the si-clause first? Any comma rule?

Yes: Si personne n’avait déplacé l’armoire, vous auriez trouvé le drap. When the si-clause comes first, use a comma. When it comes second (as in the original), you normally don’t.

Could I say this with the passive voice?

Yes: Si l’armoire n’avait pas été déplacée, vous auriez trouvé le drap. In the passive, use avait été + déplacée; the participle déplacée agrees with l’armoire (feminine singular).

What’s the difference between déplacer and bouger here?

Déplacer = move something to a different place (typical with furniture): déplacer une armoire.
Bouger = make something move/budge. Bouger l’armoire can mean “to jostle/budge it,” but for actually relocating it, déplacer is the natural choice.

Why le drap (singular)? Don’t people usually say les draps?

Le drap = one sheet.
Les draps = bed linens/sheets as a set, which is very common when talking about bedding. Either can fit, depending on context.

Is vous plural or polite singular? How would it look with tu?

Vous can be plural or formal/polite singular. With tu, you’d say: Tu aurais trouvé le drap si personne n’avait déplacé l’armoire.

Any pronunciation tips for this sentence?

Liaison in Vous auriez: it sounds like “vous-zoriez.”
trouvé ends with “-é” [ay]; drap has a silent “p.”
In personne n’avait, you’ll hear a smooth link: “personne-navè.”
l’armoire starts with a vowel; the elision makes it flow as “lar-mwar.”

Can I use the subjunctive after si here (e.g., si personne n’ait déplacé)?

No. After si in conditionals, use the indicative. Si personne n’ait déplacé is incorrect. The subjunctive can appear with other conjunctions, e.g., à condition que personne n’ait déplacé l’armoire, but that expresses a different kind of condition, not a past counterfactual.