The Pentagram

b  c d  e
  f   g
 i     j
Find a set of 10 different positive integers which can be placed on the intersections of a pentagram (five-pointed star, see figure) such that each line of four numbers has the same sum. Pick the set such that the common sum is a minimum and the largest member of the set is a minimum.

Source: Based upon Macalaster Problem 822. Found later in Henry Ernest Dudeny's 536 Puzzles & Curious Problems #393.

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