Enigma 191: Tetrahedral differences
From New Scientist #1336, 16th December 1982 [link]
The picture represents a tetrahedron, with a circle at each vertex and a square at each mid-edge. You first write a positive number at each vertex. Then at each mid-edge you write the difference between the numbers at the ends of the edge. All 10 numbers are to be different. You want the total of all 10 numbers to be as small as possible. Subject to that, you want the total of the vertex-numbers to be as small as possible.
What numbers should you put at the vertices?