``Diophantus' youth lasts 1/6 of his life. He grew a beard after 1/12 more of his life. After 1/7 more of his life, Diophantus married. Five years later, he had a son. The son lived exactly half as long as his father, and Diophantus died just four years after his son's death. All of this totals the years Diophantus lived.''

Let be the number of years Diophantus lived, and let be the number of years his son lived. Then the above word problem
gives the two equations

Solving this simultaneously gives as the age of the son and as the age of Diophantus.

**References**

Pappas, T. ``Diophantus' Riddle.'' *The Joy of Mathematics.*
San Carlos, CA: Wide World Publ./Tetra, pp. 123 and 232, 1989.

© 1996-9

1999-05-24