Sums on a Triangle and Tetrahedron

  1.       a
         / \
        b - c
       / \ / \
      d - e - f
     / \ / \ / \
    g - h - i - j
    Can you place the numbers 1-10 at the locations a-j on the triangle, such that every side (abdg, acfj, ghij) has the same sum and every internal line (bei, ceh, def) has the same sum?
  2. Can you place the numbers 1-10 on a tetrahedron, one at each corner and one on each edge, such that (1) each edge has the same sum, or (2) each face has the same sum? Is it possible to do both at once? If either is not possible, can you change one or two numbers to meet the conditions? Try to minimize the sums.
Source: Kevin King's Calculus teacher, Al Zimmermann. #1 was found later at Math Forum's MathMagic, Challenge for 10-12, Nov 28, 1999.
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