Addig illesztjük össze a képeket, amíg rájövünk, mit fejtsünk meg.

Addig ... amíg is a common Hungarian pair meaning until / up to the point when.

• addig = until then, up to that point
• amíg = until / while / as long as, depending on context

In this sentence, the pair frames the whole idea:

• Addig illesztjük össze a képeket = we keep fitting the pictures together
• amíg rájövünk... = until we realize...

So the structure is very similar to English We do X until Y happens.

Because addig is in a highlighted position at the start of the clause, and that pushes the verbal prefix össze after the verb.

Hungarian verbal prefixes often move depending on sentence structure.

• neutral: Összeillesztjük a képeket. = We put the pictures together.
• with focus/emphasis on addig: Addig illesztjük össze a képeket...

So this is not a different verb meaning; it is the same verb, just with the prefix separated because of word order.

The base verb is illeszt = fit, place into position, align.

With the prefix össze-, it becomes összeilleszt = fit together, assemble, join together.

So illesztjük össze a képeket means something like:

• we fit the pictures together
• we piece the pictures together
• we assemble the pictures

Depending on context, it could sound like a puzzle, fragments, or matching visual pieces.

Because képeket is the definite direct object.

Breakdown:

• kép = picture
• képek = pictures
• képeket = pictures (accusative, as the object)

And a means the.

So:

• a képeket = the pictures

Hungarian marks direct objects with an accusative ending, usually -t, though in plurals the full form can look different, as here: kép → képeket.

Because Hungarian is using the definite conjugation.

Hungarian verbs have two main present-tense conjugation patterns:

• indefinite: used when there is no specific object, or no object
• definite: used when the object is specific/definite

Here the object is a képeket = the pictures, which is definite, so the verb must also be definite:

• illesztünk = we fit / we are fitting (something unspecified)
• illesztjük = we fit it / them, with a definite object

So illesztjük matches a képeket.

Rájövünk means we realize, we figure out, or we come to understand.

It comes from:

• jön = come
• rájön = realize, figure out, catch on to
• rájövünk = we realize / we figure out

Literally, rájön valamire is something like come onto something, but in real usage it simply means realize or figure out.

In this sentence, rájövünk introduces the content of the realization: mit fejtsünk meg.

Because this is an indirect question, not a relative clause.

• mit = what
• amit = what / that which, usually in a relative-clause sense

Here the meaning is we realize what to solve / what we should decipher, so Hungarian uses mit:

• mit fejtsünk meg = what we should solve / decipher

If you used amit, it would point more toward that which, which is not the structure here.

Compare:

• Tudom, mit kell tennem. = I know what I have to do.
• Amit tudok, elmondom. = What I know, I will tell.

Fejtsünk is the 1st person plural imperative/subjunctive form of fejt.

In Hungarian, the imperative form also covers many subjunctive meanings, especially in clauses like:

• I don’t know what to do
• We realized what to solve
• Tell me where to go

So:

• fejtünk = we solve / we are solving
• fejtsünk = that we solve / what we should solve / what to solve

In this sentence, mit fejtsünk meg does not mean what we are solving as a plain fact. It means more like:

• what we should decipher
• what we are supposed to figure out
• what to solve

That is why Hungarian uses the subjunctive-type form fejtsünk.

Because megfejt is a prefixed verb, and the question word mit stands right before the verb in the clause.

The dictionary form is:

• megfejt = solve, decipher
• megfejteni = to solve, to decipher

But when a focused element or question word comes before the verb, the prefix often moves after it:

• neutral: Megfejtjük. = We solve it.
• question-word structure: Mit fejtsünk meg? = What should we solve?

So meg is still part of the verb, but word order splits it off.

The prefix meg- often gives a sense of completion or successful result.

• fejt by itself can mean things like unravel, work out, extract, depending on context
• megfejt specifically means solve, decode, figure out

So meg helps make this a completed, goal-oriented action: not just working on something, but actually solving it.

That is why mit fejtsünk meg means what should we solve/decipher, not just what should we work on.

It has three main parts:

1. Addig = up to that point / until then
2. illesztjük össze a képeket = we fit the pictures together
3. amíg rájövünk, mit fejtsünk meg = until we realize what we should decipher

So the logic is:

• We keep doing the first action
• until the second action happens
• and the second action includes an indirect question

A very literal structural reading would be:

• Up to that point we fit together the pictures, until we realize what we should solve.

A more natural English version would usually be something like:

• We keep putting the pictures together until we figure out what we need to solve.

That is a very typical Hungarian sentence pattern: main action + addig ... amíg clause + indirect question.