Diophantus' Riddle
``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 diedjust 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 problemgives 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.
- Nirenberg's Conjecture
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