[net.math] Mary and Ann

lew (07/16/82)

I recently got rehooked on age problems, e.g.

The sum of Mary's and Ann's age is 44. If Mary is twice as old as Ann was
when Mary was half as old as Ann will be when Ann is three times as old as
Mary was when Mary was three times as old as Ann, how old are Ann and Mary?

This was in some MIT alumni publication. After finding what I thought
was a clean general approach to this type of problem, I thought of this one:

What is the limit as N approaches infinity of the ratio of Mary's to Ann's
age, if Mary is N times as old as Ann was when Mary was N-1 times as old
as Ann was when Mary was N-2 times as old as Ann was when ... Mary was
twice as old as Ann was when Mary was as old as Ann is now.

(Typically, these problems contain a long clause which specifies the ratio
of ages, and a shorter clause which forces a unique solution.)

			Lew Mammel, Jr. - BTL Indian Hill