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2

Part of 2022 Vietnam TST

Problems(1)

Vietnam TST #2

Source: Vietnam TST 2022 P2

4/26/2022
Given a convex polyhedron with 2022 faces. In 3 arbitary faces, there are already number 26;426; 4 and 20222022 (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.
polyhedroncombinatorics