A set of six positive integers contains an arithmetic sequence of four terms, a geometric sequence of four terms, and a harmonic sequence of four terms. What are the numbers in the set when the largest member of the set is a minimum?

Note: A harmonic sequence is a sequence whose reciprocals form an arithmetic sequence. ex: ({10, 12, 15, 20} is harmonic since {1/10, 1/12, 1/15, 1/20} is arithmetic)

How about 1/2, 2/3, 1,2,3,4?

Arthimetric: 1,2,3,4
Geometric: 1/2,1,2,4
Harmonic: 1/2,2/3,1,2 (Reciprocals are 2,3/2,1,1/2)

This gives lower numbers than SilverKnight, but it may not be best!

Posted by stan on 2004-01-06 14:55:14