What is the difference between "끼리", "중에서" and "사이에서"?

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에서 is a kind of particle that describes a 'place', but it is different from 에, 에 is more focused on '(one's) state', and 에서 is more closed to '(one's) movement, motion'.

so 중에서, 사이에서., they have different meanings because of the previous words, 중 and 사이.

중(中) is from a chinese character, and this generally means the middle(center). but of course, it doesn't just have that meaning. if it is used with any group or category, it means the same as "one of them(=among/between)".

e.g.) 우리 중에서 내가 가장 강한 사람이다. i'm the strongest man among us.

사이 is a pure korean, this means the distance or interval between A and B. but if this word is used with 에서, i think it is used more often in the sense of the distance(space).

e.g.) 벌레가 틈 사이에서 나왔다. a bug came out of the crack.

끼리. this is a little different from these two. of course, 중 is also a word used when there was some... group or category, but 중 is usually used when you want to talk about a few of them.
but 끼리 is not. this is more like the members of a group sharing something with each other (time, experience, etc.). so it is similar to 'among ourselves(themselves)'

e.g.) 우리끼리 놀자 let's play among ourselves.