Я не сразу догадался, что дверь была закрыта.

Не сразу means not right away / not immediately.

So Я не сразу догадался is literally something like I didn’t figure it out immediately or I wasn’t quick to realize.

A useful point: сразу often means at once, immediately, and adding не gives the idea of a delayed realization.

Догадаться means to guess, to figure out, to realize by inference. It suggests that the speaker came to the conclusion from clues, not simply by being told.

So:

• догадался = figured out / realized
• понял = understood
• узнал = found out / learned

In this sentence, догадался works well because the idea is that the speaker eventually realized the door had been closed.

The verb is догадаться, which is the normal dictionary form.

The -ся is part of the verb itself. In many Russian verbs, -ся can make the meaning reflexive or just form a different lexical verb. Here you should learn догадаться as a whole verb meaning to realize / guess / figure out.

Its imperfective partner is догадываться.

For example:

• Я догадался = I figured it out
• Я догадывался = I was guessing / I had a suspicion

Russian past-tense verbs agree with the gender and number of the subject.

Here the subject is Я, but in the past tense Russian still marks gender:

• я догадался = I (male speaker) figured out
• я догадалась = I (female speaker) figured out

So догадался tells you the speaker is male.

Because the sentence describes a completed moment of realization.

Russian aspect matters a lot:

• догадываться (imperfective) = to be guessing, to suspect, to have an inkling
• догадаться (perfective) = to finally figure out, to realize

Here the meaning is that at some point the speaker came to the realization, so the perfective догадался is the natural choice.

Что here means that and introduces a subordinate clause.

So the structure is:

• Я не сразу догадался = I didn’t realize right away
• что дверь была закрыта = that the door was closed

This is very similar to English I didn’t realize right away that...

Both are possible, but they mean slightly different things.

• дверь закрыта = the door is closed
• дверь была закрыта = the door was closed

In your sentence, the past tense is needed because the realization refers to a past situation.

So:

• Я догадался, что дверь закрыта = I realized that the door is closed
• Я догадался, что дверь была закрыта = I realized that the door was closed

Because закрыта is the short-form passive participle/adjective, which is commonly used to describe a state:

• дверь закрыта = the door is closed

After была, Russian normally uses this short form to describe the resulting state:

• дверь была закрыта

Закрытой is the instrumental form of the long adjective/participle and would be used in different structures, for example:

• дверь была закрытой весь день = the door was closed all day

That sounds more descriptive, while была закрыта is the standard way to say was closed.

Because дверь is the subject of the clause дверь была закрыта.

In that clause:

• дверь = subject
• была = was
• закрыта = closed

So nominative is correct.

Even though English uses a passive-looking translation, in Russian this clause still has a subject: the door.

Usually it means was closed.

Depending on context, English might sometimes translate it as had been closed, but Russian itself does not have a separate past perfect form like English. The exact time relationship is often understood from context.

So out of context, the safest translation is:

• дверь была закрыта = the door was closed

Yes, potentially. Была закрыта can focus on the state of the door being closed, and it can also imply that the door was closed as a result of some action.

But the sentence does not explicitly say who closed it. It is more natural to understand it simply as the door was closed.

If Russian wanted to emphasize the person who performed the action, it would usually add that information separately.

No, Russian word order is fairly flexible, though the given version is very natural.

Я не сразу догадался, что дверь была закрыта is the neutral order.

You might also see variations for emphasis, for example:

• Я догадался не сразу, что дверь была закрыта
• Что дверь была закрыта, я не сразу догадался

These alternatives shift emphasis or sound more literary, but the original sentence is the most straightforward everyday version.

They are very close, but the emphasis can differ slightly.

• не сразу догадался = emphasizes not immediately; only later
• сразу не догадался = can sound a little more like didn’t figure it out at first

In many contexts they are almost interchangeable, but не сразу догадался is especially common and natural for didn’t realize right away.