Vietnam TST #2
Source: Vietnam TST 2022 P2
April 26, 2022
polyhedroncombinatorics
Problem Statement
Given a convex polyhedron with 2022 faces. In 3 arbitary faces, there are already number and (each face contains 1 number). They want to fill in each other face a real number that is an arithmetic mean of every numbers in faces that have a common edge with that face. Prove that there is only one way to fill all the numbers in that polyhedron.