UA-UMO 1997 Problem 113

In space are given $1997$ points. Let $M$ and $m$ be the largest and smallest distance between two of the given points. Prove that $\frac{M}{m}>9$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.