If Bill is the oldest, then Amy is not the oldest, and both statements $$\rm I$$ and $$\rm II$$ are true, so statement $$\rm I$$ is not the true one.  If Amy is not the oldest, and we know Bill cannot be the oldest, then Celine is the oldest. This would mean she is not the youngest, and both statements $$\rm II$$ and $$\rm III$$ are true, so statement $$\rm II$$ is not the true one.  Therefore, statement $$\rm III$$ is the true statement, and both $$\rm I$$ and $$\rm II$$ are false. From this, Amy is the oldest, Celine is in the middle, and lastly Bill is the youngest. This order is $$\rm E$$: Amy, Celine, Bill. 
Amy, Bill, and Celine are friends with different ages. Exactly one of the following statements is true.  $$\rm I$$. Bill is the oldest.  $$\rm II$$. Amy is not the oldest.  $$\rm III$$. Celine is not the youngest.  Rank the friends from oldest to youngest. ($$2004$$ AMC $$8$$ Problem, Question \#$$13$$) 
Options:
a. Bill, Amy, Celine 
b. Amy, Bill, Celine 
c. Celine, Amy, Bill 
d. Celine, Bill, Amy 
e. Amy, Celine, Bill 