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Find all such positive integers $n\geq2$ that there exists a set of n points on a plane, every one of which lies outside of some circle containing all the other points and having the center in one of these points.

Could you please help me? I don't even understand how am I supposed to create such a circle... As "every one of which lies outside of some circle", how, at the same time, the circle can contain "all the other points"?

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"and having the middle in one of them" dangles in your sentence. There's something in one of the points? – Dimitrije Kostic Nov 28 '11 at 15:06
What does "having the middle in one of them" mean? Does middle mean centre? To what kind of object does "them" refer? – André Nicolas Nov 28 '11 at 15:12
Sorry for the confusion, changed. – Tom Reilly Nov 28 '11 at 17:25
Could you respond on whether I decrypted the task correctly – user1708 Nov 29 '11 at 15:34
Oh, sorry, forgot about it... Yes, I believe you understood it correctly. Thank you. – Tom Reilly Nov 29 '11 at 16:29

If you intepret it such: Find all n such that we can have n points $p_i$, and n circles $C_t$, such that if $j\neq k$, then $p_j$ is contained in $C_k$, and each $C_q$ has a point $p_q$ at its center.

Then for every even $2\leq n$, we can place the points at the corners of a regular n-gon.

Proof: There is for every point a diagonalically opposite point which is further away then the others

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Thank you but is this proof enough? I mean, seems kind of short for a problem like that. – Tom Reilly Nov 29 '11 at 16:30
No its not. I will solve it tommorow if noone else does – user1708 Nov 29 '11 at 17:54
I would greatly appreciate if you do. Looking forward, then :) – Tom Reilly Nov 29 '11 at 19:25
Could you please try to prove this as you stated? I can't... – Tom Reilly Dec 1 '11 at 15:19
Dont have time, formulate it better and someone else might – user1708 Dec 1 '11 at 15:21

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