Wir können kaum raten, geschweige denn unseren Rateversuch erklären.

Kaum means hardly or scarcely.

So:

• Wir können kaum raten = We can hardly guess

It suggests that even the first, easier action is barely possible. That sets up the second part with geschweige denn, which makes an even stronger point: if we can barely do the first thing, we certainly cannot do the second, harder thing.

Geschweige denn is a fixed expression meaning something like:

• let alone
• much less
• never mind

It connects two ideas where the second one is even less possible, less likely, or more difficult than the first.

So the logic is:

• We can hardly guess, let alone explain our attempt at guessing.

A useful way to think of it is:

• first clause = already difficult or impossible
• geschweige denn
  • second clause = even more difficult / even more impossible

It is usually used after something negative or limiting, such as:

• nicht = not
• kaum = hardly
• selten = rarely
• nie = never

Because German often leaves out repeated words when they are understood from the first clause.

The full idea would be something like:

• Wir können kaum raten, geschweige denn können wir unseren Rateversuch erklären.

But that sounds clunky and unnatural. German normally omits the repeated können:

• Wir können kaum raten, geschweige denn unseren Rateversuch erklären.

English does something similar:

• We can hardly guess, let alone explain our attempt.

You do not have to repeat can in English either.

Because they depend on the modal verb können.

In German, modal verbs like:

• können = can
• müssen = must
• wollen = want to

are followed by a bare infinitive, without zu.

So:

• wir können raten
• wir können erklären

That is why you get:

• Wir können kaum raten
• ... geschweige denn unseren Rateversuch erklären

The second infinitive erklären still belongs logically to the same können, even though können is omitted.

Because after a modal verb like können, German uses the plain infinitive, not zu + infinitive.

So:

• Ich kann schwimmen.
• Wir können raten.
• Sie kann es erklären.

Not:

• Ich kann zu schwimmen ❌
• Wir können zu raten ❌

In your sentence, both raten and erklären are controlled by können, so neither takes zu.

It can mean both, depending on context.

1. raten = to guess

Example:

• Rate mal! = Guess!

2. jemandem zu etwas raten = to advise someone to do something

Example:

• Ich rate dir zur Vorsicht. = I advise you to be cautious.

In your sentence, raten clearly means guess, because there is no person being advised and the whole context is about making and explaining a guess.

This is a very common thing learners ask about, because English usually separates these meanings into different verbs, while German uses the same verb.

Rateversuch is a compound noun:

• raten / Rate- = guessing
• Versuch = attempt

So Rateversuch means something like:

• attempt at guessing
• guessing attempt
• attempted guess

German often forms nouns by combining elements like this.

That said, Rateversuch is understandable, but it is not the most everyday word. It feels a bit formal, technical, or ad hoc. A speaker might also say things like:

• unseren Versuch zu raten
• unseren Tipp
• unsere Vermutung
• unseren Erklärungsversuch (if the focus is on explaining something)

So yes, it is valid and understandable, but it is not the most common conversational choice.

Because erklären takes a direct object in the accusative case.

The noun der Rateversuch is masculine. In the accusative singular, masculine articles and similar words change:

• der Rateversuch = nominative
• den Rateversuch = accusative

With unser-, that becomes:

• unser Rateversuch = not correct here
• unseren Rateversuch = correct accusative masculine

Compare:

• Wir erklären den Versuch.
• Wir erklären unseren Rateversuch.

So unseren is there because the phrase is the object of erklären.

Because geschweige denn introduces a second coordinated part, and it is normally separated by a comma.

So the structure is:

• first statement: Wir können kaum raten
• comma
• stronger follow-up: geschweige denn unseren Rateversuch erklären

This comma is standard and helps show the pause and contrast.

Yes.

In a main clause, the finite verb is in second position:

• Wir = first element
• können = finite verb in second position

The infinitive goes toward the end:

• raten

And kaum sits in the middle field, before the infinitive:

• Wir können kaum raten.

This is a very normal German pattern with modal verbs:

• Ich kann gut schwimmen.
• Wir müssen heute arbeiten.
• Sie will das nicht sagen.

Your sentence follows the same pattern.

It is a normal educated German expression. It is not rare, but it is a bit more marked than a very plain everyday connector.

It often appears in writing, formal speech, journalism, and careful spoken German. Native speakers definitely use it, and learners should recognize it. It is the standard equivalent of let alone.

Examples:

• Ich habe keine Zeit zum Kochen, geschweige denn zum Backen.
• Er kann kaum laufen, geschweige denn rennen.

So it is not old-fashioned, but it is also not the simplest beginner-level connector.

It can be followed by different kinds of structures, not only a full clause.

For example:

With a noun phrase

• Ich habe kein Geld, geschweige denn Zeit.
• I have no money, let alone time.

With an infinitive phrase

• Er kann kaum stehen, geschweige denn laufen.
• He can hardly stand, let alone walk.

With a fuller clause

• Sie versteht das nicht, geschweige denn dass sie es erklären könnte.

In your sentence, what follows is not a full independent clause, but an abbreviated infinitive structure:

• geschweige denn unseren Rateversuch erklären

That is completely normal.

Yes, depending on what exactly you want to emphasize.

Your sentence is grammatical, but Rateversuch is a bit unusual. More natural alternatives might be:

• Wir können kaum raten, geschweige denn unsere Vermutung erklären.
• Wir können kaum raten, geschweige denn unseren Tipp erklären.
• Wir können kaum eine Vermutung anstellen, geschweige denn sie erklären.

If the goal is specifically attempt at guessing, your original sentence works, but it sounds somewhat constructed. A native speaker might choose a smoother phrase unless there is a special reason to use Rateversuch.

A useful pattern is:

• [subject] + [modal verb] + [limiting word] + [infinitive], geschweige denn + [stronger second element]

In your sentence:

• Wir = subject
• können = modal verb
• kaum = limiting word
• raten = first infinitive
• geschweige denn
• unseren Rateversuch erklären = second, even less likely action

So the sentence means:

1. We can barely do X.
2. Therefore, we certainly cannot do the harder thing Y.

This is exactly how geschweige denn is meant to work.