The Pentagram

    a
b  c d  e
  f   g
    h
 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.

Ken's Solution: 1,2,3,4,5,6,8,9,10,12. 
     5
1  10 9  4
  3    2
    12
 6      8
Solution: It can be done with 1-10, replacing 7 with 12, or 8 with 13, etc. to get a sum of 24 for each line. 12 is the minimum largest member of the set. A diagram of the solution is shown (there is no other solution - any others use exactly the same five sets of four integers, with just a configuration change.)
Solution found by Lynne Onitsuka, and several others at the Panthera Puzzle Contest.
Mail to Ken