An unpublished week

The May 7 - May 13 week was the time for the first regional event of TopCoder Open 2018 in Warsaw. The problems and results seem to be unavailable on the TopCoder website, but you can read the recap here.

On Sunday of the same week the 2017-18 season of the Open Cup was wrapped up with the Grand Prix of Bashkortostan (results with Open Cup login, top 5 on the left). The overall season standings are not yet available, but there's no doubt about the first place of team Past Glory. In this round they have reiterated how huge the gap between them and the rest of the field really is, solving all problems from first attempt in 2 hours and 24 minutes, and having almost half the penalty time of the second-placed team. Huge congratulations!

Problem I in this round was relatively standard, and yet there was a lot of room for coming up with a solution that is easy to implement, as the constraints were relatively low. You are given the coordinates of the vertices of a convex polyhedron in three-dimensional space. You need to determine the horizontal plane that separates the polyhedron's volume 1:9. The number of vertices is at most 100. How would you implement this?

Thanks for reading, and check back for more!