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Problem 245

Combinatorics Difficulty 2.0 Prove it KöMaL problem A · Hungary · 2018

The Hawking Space Agency operates $n-1$ space flights between the $n$ habitable planets of the Local Galaxy Cluster. Each flight has a fixed price which is the same in both directions, and we know that using these flights, we can travel from any habitable planet to any habitable planet.

This one wants a proof. Work it on paper, then check yourself against the publisher's own solution, linked below. Be honest about it: the record is only any use to you if it is.

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Source: KöMaL, licensed Rights held by KöMaL and the MATFUND Foundation. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.