Он сам решает задачу.

He solves the task himself.

Breakdown of Он сам решает задачу.

• он: he
• решать: to solve
• задача: the task
• сам: by himself

Questions & Answers about Он сам решает задачу.

What does сам mean in this sentence, and what nuance does it add?

Сам roughly corresponds to himself / by himself / on his own.

In Он сам решает задачу, сам adds emphasis:

• He is doing the solving himself, not someone else.
• He is doing it without help, not relying on others.

So the basic meaning He is solving the problem becomes more like:

• He is solving the problem himself.
• He solves the problem on his own.

Could you just say Он решает задачу without сам? How would the meaning change?

Yes, Он решает задачу is a perfectly correct sentence.

Difference:

• Он решает задачу – neutral statement: He is solving a/the problem (no special emphasis).
• Он сам решает задачу – emphasizes independence or contrast:
  • He, not someone else, solves it.
  • He solves it without help.

So сам adds an extra shade of meaning, but is not grammatically required.

Where can сам go in this sentence, and does the word order change the emphasis?

Common possibilities:

1. Он сам решает задачу.
   Most neutral and common. Emphasis on he himself as the doer:

   • He himself solves the problem (not his friend, not the teacher).

2. Он решает задачу сам.
   Often sounds a bit more like without help:

   • He solves the problem by himself, no one is helping.

3. Сам он решает задачу.
   Stronger, more contrastive emphasis on сам он:

   • He solves the problem himself (implying others do things differently, or someone doubted it).

The core meaning is similar in all three. Russian word order mainly shifts focus/emphasis, not basic grammar.

What is the difference between сам and один in this kind of sentence?

Сам and один are related but not identical:

• сам = himself / on his own / without help
  Focus on doing something without assistance.

  • Он сам решает задачу. – He solves the problem himself (others may be present, but they don’t help).

• один = alone / by himself (physically)
  Focus on being alone, with no one else there.

  • Он решает задачу один. – He is solving the problem alone (no one else in the room, for example).

You can combine them:

• Он сам решает задачу один. – He solves the problem himself, alone.

So:

• Use сам when you mean without help.
• Use один when you mean without other people around.

What form of the verb is решает? Which person and number is it, and how is решать conjugated in the present tense?

Решает is:

• Present tense
• Imperfective aspect
• 3rd person singular
• From the verb решать (to solve, to decide).

Present tense of решать:

• я реша́ю – I solve / I am solving
• ты реша́ешь – you solve (singular, informal)
• он/она/оно реша́ет – he/she/it solves
• мы реша́ем – we solve
• вы реша́ете – you solve (plural or formal)
• они реша́ют – they solve

So in Он сам решает задачу, the verb agrees with он (he): реша́ет.

Which aspect is решает (from решать), and how is that different from решит (from решить)?

Russian has two main aspects:

• реша́ть – imperfective (process, repeated action, general ability)
• реши́ть – perfective (single completed action, result)

Решает (from решать):

• Describes an ongoing process:
  
  • Он реша́ет зада́чу. – He is solving the problem (right now).
• Or a repeated/habitual action:
  • Он всегда сам реша́ет зада́чи. – He always solves problems himself.

Реши́т (from решить) is future, perfective:

• Focus on the result in the future:
  • Он сам реши́т зада́чу. – He will (successfully) solve the problem himself.

So решает = process / habit; решит = one completed future action with result.

If I want to say “He will solve the problem himself”, should I use Он сам решит задачу or Он сам решает задачу?

For clear future meaning with focus on the result, you should use the perfective:

• Он сам реши́т зада́чу. – He will solve the problem himself.

Он сам реша́ет зада́чу is present tense:

• He is solving the problem himself (now), or
• He (generally) solves problems himself (habit).

So:

• Future, one-time result → Он сам реши́т зада́чу.
• Present process or general habit → Он сам реша́ет зада́чу.

What case is задачу, and what is the dictionary form of this noun?

Задачу is in the accusative singular.

The dictionary (nominative singular) form is зада́ча.

Pattern:

• зада́ча – nominative singular: a problem / a task
• Он реша́ет зада́чу. – accusative singular: he solves a/the problem (direct object)

Why does задача change to задачу? How are feminine nouns in -а declined in the accusative singular?

За́дача is a typical feminine noun ending in -а.

For such nouns, the accusative singular is formed by changing -а to -у:

• Nominative: зада́ча – the subject (the problem)
• Accusative: зада́чу – the direct object (solves what? the problem)

Mini-paradigm for зада́ча:

• Nominative: зада́ча – задача сложная. (The problem is difficult.)
• Genitive: зада́чи – нет задачи. (There is no problem.)
• Dative: зада́че – к задаче. (to the problem)
• Accusative: зада́чу – реша́ет зада́чу. (solves the problem)
• Instrumental: зада́чей – с задачей. (with the problem)
• Prepositional: зада́че – о задаче. (about the problem)

So реша́ет зада́чу uses the accusative because задачу is the direct object of the verb решает.

Are there articles like “a” or “the” in Russian? How do I know whether задачу means “a problem” or “the problem”?

Russian does not have articles like a / an / the.

Задачу can be translated as either:

• a problem / a task
• the problem / the task

Which one you choose in English depends on context:

• If the problem is introduced for the first time:
  
  • Он сам решает задачу. → He is solving a problem himself.
• If both speakers already know which specific problem is meant:
  
  • Он сам решает задачу, о которой мы говорили. → He is solving the problem we talked about himself.

Russian can make it explicit with demonstratives:

• Он сам решает э́ту зада́чу. – He is solving this problem himself.

What exactly does задача mean? Is it a math problem, a task, or a general problem, and how is it different from проблема or пример?

За́дача usually means:

• A task / assignment (something to be done)
• A problem to be solved, often structured or formal:
  • school or exam problems
  • math and physics problems
  • clearly defined tasks at work

Examples:

• матема́тическая зада́ча – a math problem
• трудная зада́ча – a difficult task

Comparison:

• пробле́ма – a problem in the sense of difficulty, trouble:
  • У него пробле́мы с деньга́ми. – He has money problems.
• при́мер – literally example, but in school arithmetic it often means a simple exercise / sum:
  • реша́ть при́меры – to do simple arithmetic problems (like 2 + 2).

So:

• зада́ча – structured task/problem to be solved.
• пробле́ма – trouble, issue, difficulty.
• при́мер – example, simple exercise.

How is Он сам решает задачу pronounced, and where is the stress in each word?

Phonetically (approximate):

• Он – [on]
• сам – [sam]
• реша́ет – [rʲɪˈʂajɪt] (stress on ша́)
• зада́чу – [zɐˈdat͡ɕʊ] (stress on да́)

Stressed syllables in writing:

• Он сам реша́ет задача́? – this would mean “Is he solving the problem himself?” (with a question intonation)
• In our statement: Он сам реша́ет зада́чу.

So you say it roughly as:

• on sam re-SHA-yet za-DA-chu, with the main stresses on -ша́- and -да́-.