mondai no kaiketu ha muzukasii desu.

The sentence is built like this:

• 問題 = problem
• の = links nouns, often like of
• 解決 = solution / solving
• は = topic marker
• 難しい = difficult
• です = polite ending

So the structure is basically:

[problem + solving/solution] + is difficult

A very literal breakdown would be:

As for the solution of the problem, it is difficult
or
Solving the problem is difficult

Japanese often builds ideas with noun phrases first, then comments on them.

Here, の connects 問題 and 解決.

So:

• 問題 = problem
• 解決 = resolution / solving
• 問題の解決 = the problem’s resolution, or more naturally, solving the problem

A very common use of の is to show a relationship between two nouns. In English, this relationship is often translated as:

• of
• possessive ’s
• sometimes just by reversing the order

For example:

• 日本の文化 = Japanese culture / the culture of Japan
• 学生の本 = the student’s book
• 問題の解決 = the solution of the problem / solving the problem

So の does not always mean exactly one English word. It just links the two nouns.

Because は marks the topic of the sentence.

The topic here is not just 解決 by itself, but the whole phrase:

問題の解決は = as for solving the problem...

Then the sentence says something about that topic:

難しいです = is difficult

So the full logic is:

• Topic: 問題の解決
• Comment about the topic: 難しいです

This is a very common Japanese pattern:

X は Y です
= As for X, it is Y

Here:

問題の解決は難しいです
= As for solving the problem, it is difficult

Because 難しい is an i-adjective in Japanese. It already carries the meaning is difficult.

So:

• 難しい = difficult / is difficult

The です at the end makes the sentence polite. It does not turn 難しい into an adjective; it just adds politeness.

Compare:

• 難しい。 = It is difficult. plain style
• 難しいです。 = It is difficult. polite style

This is normal with i-adjectives:

• 高い = expensive / high
• 高いです = is expensive / is high
• 面白い = interesting
• 面白いです = is interesting

Because Japanese often uses nouns where English might use a verb.

解決 is a noun meaning solution or resolution, but in phrases like 問題の解決, it can naturally correspond to English solving the problem.

So instead of saying:

• To solve the problem is difficult

Japanese says something closer to:

• The solving/resolution of the problem is difficult

This kind of noun-based expression is very common in Japanese, especially in formal or written styles.

A more verb-like version would be:

• 問題を解決するのは難しいです。

That means Solving the problem is difficult more directly.

So your original sentence is perfectly normal, just slightly more noun-centered.

Because 問題 is not being marked as the direct object of a verb here.

If you had a verb like 解決する (to solve), then you would say:

• 問題を解決する = to solve the problem

But in your sentence, 解決 is being used as a noun inside the noun phrase 問題の解決.

So:

• 問題を解決する = solve the problem
• 問題の解決 = the solution/resolution of the problem, or solving the problem

Since there is no verb 解決する in the sentence, there is no need for を here.

They are very similar, but not identical in nuance.

問題の解決は難しいです

• more noun-based
• can sound a little more formal or abstract
• focuses on the resolution/solving as a concept

問題を解決するのは難しいです

• more verb-based
• feels more direct
• focuses on the act of solving the problem

In many situations, both can be translated as Solving the problem is difficult.

So the difference is mostly about style and phrasing, not a big difference in core meaning.

Yes, in a way.

Japanese often does not state subjects the way English does. Instead, it gives a topic with は and then says something about that topic.

So English may need a subject like:

• It is difficult
• Solving the problem is difficult
• The resolution of the problem is difficult

But Japanese can simply say:

• 問題の解決は難しいです

There is no separate word for it here, and none is needed.

By itself, 問題 does not show singular or plural.

So depending on context, it could mean:

• a problem
• the problem
• problems
• the problems

In this sentence, English might translate it as the problem or a problem, depending on the situation.

Japanese usually leaves number unstated unless it matters.

Because Japanese does not have articles like English a, an, or the.

That means 問題 could mean:

• a problem
• the problem

and 問題の解決 could mean:

• a solution to the problem
• the solution to the problem
• solving the problem

The exact English article depends on context, not on a specific Japanese word.

This is one of the biggest differences between English and Japanese.

It is pronounced:

mondai no kaiketsu wa muzukashii desu

A rough pronunciation guide:

• 問題 = mon-dai
• の = no
• 解決 = kai-ketsu
• は is written ha but pronounced wa
• 難しい = mu-zu-ka-shii
• です = desu (often sounding closer to des in natural speech)

So the whole sentence sounds like:

mon-dai no kai-ketsu wa mu-zu-ka-shii des(u)

Yes, it is natural.

It sounds a bit formal or written because of the noun phrase 問題の解決, but it is absolutely normal Japanese.

Depending on style, a speaker might also say:

• この問題を解決するのは難しいです。 = Solving this problem is difficult.
• 問題を解決するのは難しいです。 = Solving the problem is difficult.

Your original sentence is especially natural in explanations, writing, school contexts, business contexts, or formal discussion.