A megoldás egyedi.

A is the definite article, meaning the.

Hungarian has two forms of the definite article:

• a before consonant sounds
• az before vowel sounds

So:

• a megoldás = the solution
• az ötlet = the idea

Since megoldás starts with m, you use a.

Yes, from an English point of view, it may look like is is missing.

In Hungarian, the present-tense verb van = is is usually omitted in the 3rd person singular and 3rd person plural when the sentence links a subject with a noun or adjective.

So:

• A megoldás egyedi. literally looks like The solution unique.
• But it means The solution is unique.

The verb does appear in other tenses:

• A megoldás egyedi volt. = The solution was unique.

Because here egyedi is the predicate adjective of the sentence, not an adjective directly attached to the noun inside a noun phrase.

Compare:

• egyedi megoldás = a unique solution
• A megoldás egyedi. = The solution is unique

So:

• adjective before the noun = it describes the noun directly
• adjective after the noun = it is part of the statement about the noun

Yes, but they mean different things grammatically.

• egyedi megoldás = a unique solution
  This is just a noun phrase, not a full sentence.

• A megoldás egyedi. = The solution is unique.
  This is a complete sentence.

So Hungarian can put the adjective before the noun, but that gives a different structure from the sentence you have here.

Egyedi usually means something like:

• unique
• individual
• distinctive
• custom-made or tailored in some contexts

With megoldás, it often suggests that the solution is not standard, but rather special or specifically suited to a situation.

So the exact English translation can vary a little depending on context, but unique is a very common choice.

Yes, it is related historically and in meaning.

Egy means one or a/an, and egyedi carries the idea of being individual, single, or one of a kind.

That said, it is best to learn egyedi as its own adjective with the meaning unique / individual / custom rather than trying to build its meaning from egy every time.

Yes, that is also grammatical.

The difference is mainly emphasis.

• A megoldás egyedi. = neutral statement
• Egyedi a megoldás. = stronger focus on egyedi

Hungarian word order is flexible, and moving a word to the front often gives it special focus. So Egyedi a megoldás can sound more like:

• The solution is unique
• It’s the solution that is unique
• Unique is what the solution is, in a more literal sense of emphasis

A rough English-friendly pronunciation is:

aw MEH-gol-daash EH-dyeh-dee

A few useful pronunciation points:

• s in Hungarian sounds like English sh
• gy is a soft consonant, roughly like dy
• á is a long vowel
• the stress is on the first syllable of each word

A more precise IPA pronunciation is approximately:

[ɒ ˈmɛɡoldaːʃ ˈɛɟɛdi]

Megoldás comes from the verb megold = to solve.

Hungarian often uses the suffix -ás / -és to make a noun from a verb. So:

• megold = solve
• megoldás = solution / solving

This is a very common word-building pattern in Hungarian.

Not here.

Hungarian does not have grammatical gender, so there is no masculine/feminine/neuter adjective agreement to worry about.

In this sentence, both words are singular, so egyedi stays unchanged.

If the subject were plural, the predicate adjective would usually become plural too:

• A megoldások egyediek. = The solutions are unique.

But in A megoldás egyedi, singular egyedi is exactly right.