Originally posted by geepamoogleBuild them all at the vertices of a tetrahedron shape inside a freely rotating sphere. Each house will be equidistant from the others, and no one person has to take the stairs every time they want to get inside - everyone just rotates the sphere until their house appears at the entrance (for fairness' sake).
My hint. It's not possible in the Midwest Plains. Figure out why, and you're one step closer to a solution.
Originally posted by uzlessTechnically, in this case the houses will be a little farther from the house in the opposite corner than the ones in the adjacent corners.
Or you could just build the houses in a square so they are all touching each other in the centre like this....
Originally posted by PBE6Or just find a suitable hill.
EDIT: D'oh...instead of having this ungainly sphere contraption, why not build the houses at the vertices of a tetrahedron inscribed in the sphere that is the Earth? (This assumes that the Earth is perfectly spherical, of course.)
Originally posted by FabianFnasThe hill idea is that one's at the peak and the other three lower down at equal elevations to one another, thus making a tetrahedron. However this fails because the one at the top is different than the others.
I think geepamoogle have a correct answer. Thanks for not reveal the solution too quickly.
uzless had also a solution, the trivial one, but well within the definition about distances. Zero distance is also a distance.
PBE6 suggested a tetrahedron, and this is the non-trivial solution. If you in any way can place the four houses at the corners of a t ...[text shortened]... ll. Would you elaborate this a little, mtthw?
(Have I forgot any other with a good solution?)
Originally posted by AThousandYoungYou mean, it fails because it is not fair that one of the friends has downhill to others and the others not? Hm...
The hill idea is that one's at the peak and the other three lower down at equal elevations to one another, thus making a tetrahedron. However this fails because the one at the top is different than the others.