If anybody is competing in the contest, this may be helpful as a starting point!
Open Problems in Computational Geometry Listed by Erik Demaine, Joseph Mitchell, Joseph O'Rourke in 2024
And also the popular list below, which contains some of the frontier problems and undefeated beasts that have remained unsolved for decades, some even for centuries.
https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_m...
Caution: Solvability is not guaranteed!