один/одна/одно/одни

1. Grammatical Agreement and Declension
Unlike other cardinal numbers, один behaves like an adjective and agrees with its noun in gender, number, and case. Notice that the fleeting vowel 'и' is present in the masculine nominative singular (один) but drops out in all other forms, including the neuter (один → одного, одно). Additionally, the stress always falls on the ending in all forms except the masculine nominative.

In the accusative case, it follows the animacy rule: for masculine and plural nouns, use the nominative form for inanimate objects (один/одни) and the genitive form for animate beings (одного/одних).

2. Compound Numbers
In compound numbers ending in 1 (like 21, 31, 101), the word один still agrees with the noun's gender (or number, for pluralia tantum nouns, e.g., двадцать одни часы). For regular, countable nouns, the noun itself stays in the nominative singular (e.g., двадцать один день) only when the phrase is in the nominative or inanimate accusative case. In oblique cases, the noun remains singular but declines to match the case of the number (e.g., с двадцатью одним студентом). The number 11 (одиннадцать) behaves differently: like numbers 5-20, it governs the genitive plural in the nominative and inanimate accusative cases, but in oblique cases, the noun goes into the plural and agrees with the case of the number (e.g., с одиннадцатью студентами).

3. The Plural Form (одни)
The plural form одни is used:

• With pluralia tantum nouns: одни часы (one watch).
• With nouns that come in pairs to mean 'one pair of': одни носки (one pair of socks) or одни перчатки (one pair of gloves).
• To mean 'only': Там одни ошибки (There are only mistakes there).
• To mean 'some' (contrasted with others): Одни... другие... (Some... others...).

4. Meaning 'Alone'
The word один is used to mean 'alone' or 'by oneself'. In this sense, it must agree with the subject it describes: Он один (He is alone), Она одна (She is alone), Они одни (They are alone).

5. 'A certain' and 'One of'
Один can mean 'a certain' or 'a' when introducing someone or something new: один мой друг (a certain friend of mine). It is also used in the construction один из + genitive plural to mean 'one of': один из студентов (one of the students).

6. Один vs. Раз
Use раз for abstract counting (1, 2, 3...) or when saying 'once'. Use один whenever you are counting specific objects or people.

7. Omission of '1' (Translating 'a/an')
Unlike English, which frequently uses 'a' or 'an', Russian typically omits the number 1 unless you want to emphasize the exact quantity. For example, Я купил билет means 'I bought a ticket', whereas Я купил один билет emphasizes 'I bought one ticket'.

8. Common Set Phrases
The word один appears in several highly frequent idioms and set phrases. Some common examples include:

• один и тот же (the exact same one)
• один за другим (one after another)
• один на один (one on one / face to face)