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IMO 1968 — Shortlist problems Question 20

IMO Shortlist · IMO 1968 — Shortlist problems

Question 20

(CZS 1) Given $n$ $(n\ge3)$ points in space such that every three of them form a triangle with one angle greater than or equal to $120^\circ$, prove that these points can be denoted by $A_1,A_2,\ldots,A_n$ in such a way that for each $i,j,k$, $1\le i\lt j\lt k\le n$, angle $A_iA_jA_k$ is greater than or equal to $120^\circ$.