We can spot that Jack\textquotesingle s statement and Jimmy\textquotesingle s statement contradict each other, so one of them is telling the truth. Therefore, Sarah tells a lie. 
Jack, Sarah, and Jimmy participated in a maths competition.  Jack says: "I won the competition."  Sarah says: "I didn\textquotesingle t win the competition."  Jimmy says: "Jack didn\textquotesingle t win the competition."  Only one of them told the truth. Who won the maths competition? ． 
Options:
1. $$$$Jack 
2. Sarah 
3. Jimmy 