Today we will talk about another use of по, and this one is a weird one. When you express the idea of giving each individual in a group of people the same quantity of something, you express that quantity after the preposition по. In English we express the idea with the words each or apiece:

You will notice that in those sentences the dative case was used after по. You are probably thinking, “No problem. I'll just memorize that по in the distributive sense is used with the dative.” You poor sucker. The Russian language is about to kick you in the teeth. Consider the following sentences:

Pop quiz: what case is used after по when more than one object is distributed? Since два щенка and две кошки occur after по, any normal human being would say that it is the nominative case. There was an old assumption, however, that no preposition can govern the nominative case, which is mostly true in Indoeuropean languages. To be frank, the issue is complicated for reasons that are beyond the goals of this blog. The practical answer is this: when a number other than one is used after по, the number is in the nominative case. The noun that number quantifies shows up in the genitive singular if the number is полтора/ы, два/е, три or четыре, and in the genitive plural for other numbers. So here is a rule of thumb for first- and second-year Russian students:

Distributive по: uses the dative case when talking about a single item; uses nominative case of numbers other than one.

If you want to pursue the question of what the case actually is that по governs, start with Igor Melchuk's excellent book ... Melchuk is a grammatical god to whom I have erected a shrine (along with his publisher... ) in my home. I make a small offering to them every day in a brass bowl. The fire is fueled by pages ripped from People Magazine, which richly deserves to be burned, and the sacrifice is made of my own blood and hair, accompanied by me singing «Я хочу быть с тобой» by Nautilus Pompilius.