Five women are standing on platforms on a stage. The shortest woman measures 5 feet, 0 inches. Each woman is a different height, and the difference in height between any pair of women is a different integral number of inches. There are four platforms on the stage, raising the shorter women to the height of the tallest. If the total platform height is a minimum, what are the heights of the other four women?
Extensions: Some obvious extensions suggest themselves. Repeat the problem for 3,4,6,7,8 women. Is there any pattern or procedure which helps in the solutions?