Мы не разгадали головоломку, не говоря уже о шифре.

Разгадали is the past tense plural form of разгадать.

• разгадать = to figure out, solve, decipher
• мы разгадали = we solved / we figured out

It is plural because the subject is мы (we).

This verb is also perfective, so it presents the action as a completed whole: we did not solve it. In this sentence, that completed-result meaning fits well.

This is mainly about aspect.

• разгадать (perfective) = to solve, to succeed in figuring out
• разгадывать (imperfective) = to be solving, to try solving, to solve in a repeated/ongoing sense

Мы не разгадали головоломку means We didn’t solve the puzzle — the result was not achieved.

If you said Мы не разгадывали головоломку, that would usually mean We weren’t trying to solve the puzzle or We didn’t work on the puzzle, which is a different idea.

So the perfective verb is used because the sentence is about failure to reach the result.

Because головоломка is the direct object of разгадали, it takes the accusative case.

Dictionary form:

• головоломка = puzzle, brainteaser

Cases:

• nominative: головоломка
• accusative: головоломку

So:

• Мы разгадали головоломку = We solved the puzzle

This is normal for a feminine noun ending in -а.

Не говоря уже о is an idiomatic expression meaning:

• let alone
• not to mention
• never mind

In this sentence:

• Мы не разгадали головоломку, не говоря уже о шифре.
• We didn’t solve the puzzle, let alone the cipher.

The idea is: if we couldn’t do the easier or more basic thing, then the harder or more extreme thing is even less likely.

Literally, не говоря уже о is something like not even speaking of or not to speak already of, but you should learn it as a fixed expression.

Because the expression не говоря уже о requires о + prepositional case.

So:

• шифр = dictionary form
• о шифре = about the cipher / let alone the cipher

This is because the phrase is built on говоря о... = speaking about...

Examples:

• не говоря уже о деньгах = let alone money
• не говоря уже о времени = let alone time
• не говоря уже о шифре = let alone the cipher

So the prepositional case after о is exactly what you should expect.

For learning purposes, it is best to treat не говоря уже о as one fixed idiomatic chunk.

Technically, говоря is a verbal adverb (sometimes called a gerund in learner materials), from говорить. But in this expression, Russian speakers usually process it as a set phrase meaning let alone / not to mention.

So instead of analyzing it every time, it is more useful to memorize:

• не говоря уже о + prepositional

That will help you produce correct Russian more naturally.

Because не говоря уже о шифре is a parenthetical/add-on expression, separated off by a comma.

Russian normally writes this phrase with a comma when it adds an afterthought like let alone...

So:

• Мы не разгадали головоломку, не говоря уже о шифре.

The comma signals that the second part comments on or strengthens the first part.

Yes, very often.

Russian often drops subject pronouns when the verb form already makes the subject clear.

So both are possible:

• Мы не разгадали головоломку, не говоря уже о шифре.
• Не разгадали головоломку, не говоря уже о шифре.

The version with мы is a bit more explicit and can add emphasis or clarity. Russian uses pronouns less often than English does.

Because разгадать works well with things that involve figuring out hidden meaning, logic, or a secret.

Common objects of разгадать include:

• головоломку = a puzzle
• загадку = a riddle / mystery
• шифр = a cipher / code
• тайну = a secret, mystery

So разгадать is a very natural verb here.

A verb like решить can also mean solve, but it is often more natural for:

• problems
• tasks
• equations
• questions

For a puzzle, riddle, or cipher, разгадать is especially appropriate.

Both can sometimes be translated as code, but they are not always the same.

• шифр usually means cipher, something encrypted
• код can mean code more broadly: a code, password, numeric code, computer code, etc.

In this sentence, шифр suggests something that has to be deciphered, which fits разгадать very well.

So the English translation cipher is often the best choice here.

Very often, yes, but not absolutely always.

It is especially common after a negative or limiting idea:

• Он не знает французского, не говоря уже о китайском.
• He doesn’t know French, let alone Chinese.

That pattern is exactly what we have here:

• Мы не разгадали головоломку, не говоря уже о шифре.

The second item is presented as even less likely, more difficult, or more extreme than the first.

Yes, but the tone is slightly different.

In this sentence:

• let alone is the strongest and most natural choice
• not to mention is possible, but can sound a bit weaker in English

So:

• We didn’t solve the puzzle, let alone the cipher. ← best
• We didn’t solve the puzzle, not to mention the cipher. ← understandable, but less idiomatic in English

So for this sentence, let alone is probably the best translation.

It breaks down like this:

• Мы = we
• не разгадали = did not solve / figure out
• головоломку = the puzzle
• не говоря уже о шифре = let alone the cipher

So the structure is:

[subject] + [negative past verb] + [object], + [idiomatic intensifying phrase]

The logic is:

1. We failed at the first thing.
2. Therefore the second thing was even more out of reach.

That is why the sentence feels natural and emphatic.