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There is a (borrowed) word "тетрада" in Russian, whih means "a group of four elements".

Well it's not annoying, it's just funny when they use completely unrelated "Я" letter instead of "R".

This game was named "tetris" because each falling piece consists of four squares, I guess. "tetris" is not a Russian word.
Pravit, "тетрадь", not "тетрядь". But the name "tetris" was not derived...