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In one formal texts I encountered this "в общей сложности" used when addressing the total amount of something. An example context below:

В общей сложности страны СНГ продемонстрировали падение числа изучающих русский ...

I was told that the в общей сложности is simply synonym for в итоге or в общем, even though there is the word сложность included. Does the word add any specific information to the context, and what is the logic behind this adverb? I assume this is used as a stable structure.

Additional question: are these kind of structures common in Russian? And are their meaning usually logically understandable, or are they mostly distinct cases that just need to be memorized?

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"В общей сложности" is indeed a synonym of "в итоге", "в общем" and "в сумме", but, as usual, there are little nuances.

"В общей сложности" used when we are summarizing some measure that was not originally intended to be summarized, or if the process of this summarization is not mathematically sound.

This is roughly a "precision rank" among these phrases:

  1. "в итоге", "в сумме" (precise math)
  2. "в общей сложности" (approximate math, or suggestion that precise math is not needed here)
  3. "в общем" (mostly opinion based)

In your example "В общей сложности страны СНГ продемонстрировали падение числа изучающих русский" it is not clear that initial goal of this exercise was finding a total number of people studying Russian. The goal (total number) is apparently introduced just in this sentence, and that's why "в итоге" and "в сумме" is less appropriate here. "В общем" would be still good here.

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I believe «сложность» here is a verbal noun derived from «сложить» -- add together, and the construct means "having added all together". «Сложность» alone is not commonly used in that sense though; «в общей сложности» is a set phrase.

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    This. Compare "глаголы, сложные с esse" in classical philology - it means compounds with esse not some particularly difficult verbs. – Viridianus Mar 28 at 10:40
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As recently as 150 years ago, сложность used to mean "totality, entirety", something that in the modern language is usually conveyed by the word совокупность:

  • Но судя о людях и делах людских, должно брать в соображение не отдельные черты или происшествия, а всю их сложность

  • Откройся, мать наша, безмерная Русь, мир-государство, во всей полноте своей! Покажи нам всю сложность, все части своего разнообразного состава.

  • Какая сложность элементов выражена в этой сцене: уездная барыня, устарелая кокетка, смешная мать!

The English word "complex" (literally "intertwined"), which came to mean both "hard" and "composed of multiple parts", had undergone a similar evolution.

В общей сложности is a set phrase which is using this outdated meaning.

This phrase means "in total", "in all entirety".

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