ASU 086 All Soviet Union MO 1967 8 lamps in 8 points of space
Source:
June 20, 2019
3D geometrygeometry
Problem Statement
a) A lamp of a lighthouse enlights an angle of degrees. Prove that you can turn the lamps of four arbitrary posed lighthouses so, that all the plane will be enlightened. b) There are eight lamps in eight points of the space. Each can enlighten an octant (three-faced space polygon with three mutually orthogonal edges). Prove that you can turn them so, that all the space will be enlightened.