24

Part of 2019 Sharygin Geometry Olympiad

Problems(1)

Sharygin CR 2019 P24

Source: Sharygin CR 2019 P24 (Grade 10 - 11)

Two unit cubes have a common center. Is it always possible to number the vertices of each cube from

1

8

so that the distance between each pair of identically numbered vertices would be at most

4/5

? What about at most

13/16