Numerals after prepositions

Many learners are taught that "numerals 5 and above always take the genitive plural." This is a myth! That rule only applies in the Nominative and Accusative cases.

1. Prepositions assigning Genitive, Dative, Locative, or Instrumental
When using prepositions like od (Gen), k (Dat), o (Loc), or s (Ins), the preposition governs the whole phrase. Both the numeral and the noun must be in that case. (Note: With Genitive prepositions like od, z, or do, the noun will be in the Genitive plural—e.g., do pěti dnů. This looks like the 'myth' mentioned above, but the noun is in the Genitive because of the preposition, not because the numeral forced it!)

• Numerals 1–4: Fully decline. The numeral 1 (jeden/jedna/jedno) declines like the pronoun ten/ta/to and must fully agree in gender, number, and case with the noun (e.g., o jednom studentovi, s jednou studentkou). Note that dva and oba use historical dual forms: Gen/Loc dvou, Dat/Ins dvěma. Tři and čtyři also have irregular forms (Gen tří/čtyř, Loc třech/čtyřech, Dat třem/čtyřem, Ins třemi/čtyřmi). Also, prepositions often vocalize before 2, 3, and 4 (e.g., ve dvou, ze tří, se čtyřmi).
• Simple Numerals 5–99: They take a single -i ending for all four of these cases (e.g., pěti, šesti, deseti, dvaceti).
• Hundreds and above: Sto, tisíc, and milion generally decline like nouns (patterns město, stroj, hrad). Note that for 200, the first part uses historical dual forms (dvou, dvěma), while the second part uses regular plural forms of sto (e.g., Gen dvou set, Loc dvou stech, Dat dvěma stům, Ins dvěma sty). When sto or its multiples (200, 300, etc.) are followed by a counted noun, they are frequently left undeclined in oblique cases (e.g., o sto lidech instead of the fully declined o stu lidech, or o dvě stě lidech instead of o dvou stech lidech). The word tisíc has a dual behavior across all oblique cases: it can act as a pure noun, forcing the counted noun into the Genitive plural (e.g., Instrumental s tisícem lidí, Dative k tisíci lidí), or it can act as a numeral, where both it and the counted noun agree in case (e.g., Instrumental s tisíci lidmi, Dative k tisíci lidem).

Example: Mluvili jsme o pěti nových studentech. (We talked about five new students. – Locative: both pěti and studentech are in the locative).

2. Prepositions assigning the Accusative
When using prepositions like pro, na, za, the numeral takes the accusative form. For numerals 1–4, the noun simply takes the Accusative case. However, for simple numerals 5+, the accusative is identical to the nominative (e.g., pět). Because the numeral acts as the head here, the noun must take the Genitive plural.
Example: Mám dárek pro deset dětí. (I have a gift for ten children. – Accusative: deset forces dětí into the genitive plural).

3. Compound Numerals (21–99)
Compound numerals can be written in two ways, affecting declension:

• One-word forms (e.g., pětadvacet): Decline like simple numerals (e.g., Locative o pětadvaceti studentech). In the Accusative, they force the Genitive plural (pro pětadvacet studentů).
• Two-word forms (e.g., dvacet pět, dvacet dva): The parts decline separately. If ending in 1–4, the final element declines fully (e.g., Locative o dvaceti dvou studentech). In the Accusative, numbers ending in 1 can take the accusative singular (pro dvacet jednoho studenta) or act as an uninflected quantifier taking the Genitive plural (pro dvacet jedna studentů / dětí), which is very common in colloquial speech, though formal writing prefers fully declined or one-word forms. Those ending in 2–4 can also take the Genitive plural or agree in the Accusative plural (pro dvacet dva studenty / studentů).

4. Spoken vs. Written Czech
While forms like dvěma and pěti are strictly required in standard Czech, colloquial spoken Czech (Common Czech) heavily favors non-standard instrumental endings like s obouma, s dvouma, s třema, se čtyřma, s pětima. Furthermore, in informal spoken Czech, numerals 5 and above are frequently left completely undeclined after prepositions (e.g., s pět lidma, před dvacet lety).