Think of stars as like people, with a childhood, a middle age, and an old age.  Suppose that their characteristics, such as color, size, composition, and brightness, change with age so that we can tell their age (just like people change with age and we can tell old from the young).  With people, there are always new ones being born and old ones dying so that we stay roughly in balance.  Suppose stars are this way too.  Now consider people:  if each year one new person is born and one old person dies (no one dies until they are old in this thought puzzle), and you have 18 children, 42 middle aged folks, and 15 oldsters, how long does it take for a child to grow up (answer)?.

If only one is born each year, and if there are 18, then it must take them 18 years to grow up.  Likewise, each spends 42 years middle aged, and 15 years in old age.

You can think of it this way:  Let one be born each year.  Each year the number of children will increase by one until there are 18 children.  Then, in the 19th year, one new child is born, but one old child "grows up", thus keeping the number steady at 18, the number of years spent as a child.  Similar reasoning shows that each spends 42 years middle aged, before becoming old, and 15 years old before dying.

This illustration is clearly simplified from what would be done in an actual investigation of the life cycle of stars (or people) because, for example, not all people live exactly the same length of time, nor are all stars exactly alike.  But it illustrates conceptually how life cycles can be figured out by looking at a steady-state population in a situation where it is impossible to observe an entire life cycle of any individual.

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