по + Numeral (Distributive)

Distributive по indicates that a quantity is assigned to every member of a group. Its case government is highly specific:

1. The Number One:
Always takes the Dative case, and the following noun is also in the Dative case. The numeral must agree in gender with the noun. Example: по одному яблоку (one apple each).

2. Numbers 2, 3, and 4:
These take the Accusative case, while the following noun is in the Genitive Singular. Crucially, even for animate nouns, the inanimate form of the numeral is used. Note that два has a feminine form две which must be used with feminine nouns (e.g., по две кошки). Example: по три человека (three people each).

3. Numbers 5 and above:
In modern standard Russian, these take the Accusative case, and the following noun is in the Genitive Plural (e.g., по пять рублей, по сто граммов). The Dative case (e.g., по пяти рублей, по сорока человек) is considered bookish or formal. Note that 90 and the round hundreds 100, 200, 300, and 400 only take the Accusative case (e.g., по девяносто рублей, по сто рублей, по триста билетов). For large round numbers like 500–900, the Accusative (e.g., по пятьсот) is the modern standard, and the formal Dative is the highly unusual mixed form по пятисот.

4. Large Numbers (1,000, 1,000,000):
Words like тысяча, миллион, and миллиард typically take the Dative case, and the noun is in the Genitive Plural. Example: по тысяче рублей (a thousand rubles each).

5. The Numeral Полтора (One and a half):
The numeral полтора (or полторы for feminine) takes the Accusative case, and the noun is in the Genitive Singular. Example: по полтора часа (an hour and a half each).

6. Collective Numerals and Quantifiers:
Collective numerals take the Accusative, and the following noun is in the Genitive Plural (e.g., по двое студентов, по трое). The quantifiers много, мало, and несколько can take the Accusative (по много, по мало, по несколько) or special distributive forms (по многу, по малу, по нескольку), and the following noun is in the Genitive Plural (e.g., по нескольку часов, по много раз).

7. Compound Numerals:
The case of a compound numeral phrase is determined by its components. If the compound numeral contains words that strictly dictate the Accusative case in this pattern (such as 2, 3, 4, 90, 200, 300, or 400) anywhere in the phrase, the entire numeral phrase is forced into the Accusative case (e.g., по двести тридцать пять рублей). If the compound numeral ends in один, the phrase follows the Dative rule (e.g., по двадцать одному рублю). Otherwise, the Accusative is the modern standard for the entire phrase.