After his death, the estate of an eccentric millionaire was to be divided between his two sons. His five Rolls Royces were of particular interest to the sons, but they faced quite a dilemma. The oldest son was to receive 1/2 of the estate and the youngest was to receive 1/3. However, since 2 and 3 do not divide 5, the sons could not figure out how to divide the cars equitably. A dear friend of the deceased man came to the rescue. She put her Rolls Royce into the collection, making a total of 6 cars. Now the sons could finally claim their inheritance: half of the six (3) went to the oldest son, one-third of the six (2) went to the youngest son, and the helpful woman took her own car back. Content with the arrangement, the sons happily went their own ways.

1. Several months after the agreement, the two sons met to reminisce about their father. Each began to argue that he did not receive his fair share of the inheritance: neither could explain the thinking of their father's friend. Did either son get ripped off? Explain.
2. A fraction with only the digit 1 in the numerator is called a unit fraction. Sums involving distinct unit fractions, such as

   1 2 + 1 3 + 1 6 ,

   are called Egyptian fractions. Find out why and write a paragraph or two to summarize your conclusions.
3. Write an inheritance problem that involves unit fractions and at least three beneficiaries.
4. In 1202, Fibonacci proved that any rational number P/Q could be written as an Egyptian fraction. Earlier in this project, we saw that 5/6 can be written as an Egyptian fraction in the form

   5 6 = 1 2 + 1 3 .

   Write 13/18 as an Egyptian fraction involving at least three unit fractions.