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Судья решил начислить каждой команде по одному очку.

Судья решил начислить каждой команде по одному очку.
The judge decided to award one point to each team.
From Lesson 389:Distributive numbers (по)·Russian

Questions & Answers about Судья решил начислить каждой команде по одному очку.

Why are одному and очку in the Dative case here?
This is the distributive use of по (meaning 'each'). In Russian, when expressing 'each' with the number 1 (as well as 5 and above), по requires the Dative case. So the neuter noun очко becomes очку, and the numeral одно becomes одному. If the judge had awarded 2 points, it would be по два очка, using the Accusative.
Is каждой команде also in the Dative case because of по?
No, it is Dative for a completely different reason. It is the indirect object of the verb начислить (to award points to each team). In this sentence, we happen to have two Dative phrases back-to-back, but only одному очку is triggered by по.
What exactly does начислить mean compared to other words for 'give' or 'add'?
Начислить specifically means 'to credit', 'to accrue', or 'to calculate and award'. You will see it mostly in official, financial, or numerical contexts, such as crediting points in sports, calculating interest in a bank account, or adding a bonus to a salary.
Why do we use одному instead of одной?
The noun for 'point' here is очко, which is neuter. The numeral 1 must agree with the noun's gender, so we use the neuter Dative form одному (which happens to look identical to the masculine Dative). If the noun were feminine, like монета (coin), it would be по одной монете.

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