Addig próbáljuk kinyitni a számzárat, amíg sikerül.

It is a very common Hungarian pair meaning until.

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

Together, addig ... amíg means until in the sense of continue something up to the point when X happens.

So here:

Addig próbáljuk kinyitni a számzárat, amíg sikerül.
= We keep trying to open the combination lock until we succeed.

Because Hungarian is using the definite conjugation here.

The object is a számzárat = the combination lock, which is definite. When Hungarian has a verb plus an infinitive, and that infinitive has a definite object, the finite verb is often also put in the definite form.

So:

• próbálunk = we try / indefinite
• próbáljuk = we try it / we try to do it with a definite object involved

Compare:

• Próbálunk kinyitni egy számzárat. = We are trying to open a combination lock.
• Próbáljuk kinyitni a számzárat. = We are trying to open the combination lock.

Because Hungarian says try to do something with próbál + infinitive.

So:

• próbálni = to try
• kinyitni = to open
• próbáljuk kinyitni = we try to open

This is very similar to English try to open.

The ending -ni is the normal infinitive ending in Hungarian.

kinyitni means to open.

It is built from:

• nyitni = to open
• ki- = a verbal prefix (preverb)

In many cases, ki- adds a sense of opening something up fully or getting it open. With things like doors, boxes, locks, and windows, kinyitni is very common and natural.

So:

• nyitni = open
• kinyitni = open up / get open

In this sentence, kinyitni a számzárat means to open the combination lock.

Because it is the direct object, so it takes the accusative ending -t.

• számzár = combination lock / code lock
• a számzár = the combination lock
• a számzárat = the combination lock as the object of the verb

So Hungarian marks the object clearly with -t.

Because Hungarian usually does not need subject pronouns when the verb ending already shows the subject.

Here, próbáljuk already tells you the subject is we.

So Hungarian often leaves out mi = we unless it is needed for emphasis or contrast.

For example:

• Próbáljuk kinyitni... = We are trying to open...
• Mi próbáljuk kinyitni... = We are the ones trying to open... / extra emphasis

This is a very natural Hungarian use of sikerül.

sikerül means it succeeds / it works / one manages to do it, depending on context.

In this sentence, the thing that succeeds is understood from the previous clause: opening the lock.

So:

• amíg sikerül literally feels like until it succeeds
• natural English: until we succeed or until we manage it

Hungarian often leaves that understood rather than repeating the whole action.

Yes. amíg can mean:

• while
• as long as
• until

The exact meaning depends on context.

But when it appears with addig, as in addig ... amíg, it very strongly suggests until.

So in this sentence, amíg is not understood as while. It is clearly part of the until structure.

Yes, but Hungarian word order is also flexible.

Starting with Addig is very natural because it sets up the time frame right away: until that point.

So the sentence structure highlights the idea of continuing the action up to a certain result:

Addig próbáljuk kinyitni a számzárat, amíg sikerül.

A different word order is possible in Hungarian, but this version is a very normal and useful pattern to remember.

A very natural English rendering is:

We keep trying to open the combination lock until we succeed.

That captures the idea best. Hungarian is not focusing on just one attempt, but on continuing the attempts up to the point of success.