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. |

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.) |

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