KöMaL 2018 B4930

Every inhabitant of a village belongs to one of three religious faiths: they either worship the Sun God, the Moon God or the Earth God. Regulations of these faiths require that a shrine should have the minimum possible total distance from all the houses of the village (whatever the faith of those living in the houses). Given that the worshippers of the Sun God already have a shrine in the village, and those of the Moon God have one, too, show that the worshippers of the Earth God can also build a shrine for themselves. (The village lies on flat terrain, and the shrines and the houses of the village can be considered pointlike.)