I have a packet of biscuits which contains between $400$ and $800$ biscuits.  If I put them into piles of $5$, I have one left over.  If I put them into piles of $6$, I have two left over.  If I put them into piles of $11$, I have seven left over.  How many biscuits do I have? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem->Step-by-step Calculation