Alison has a large number of coloured pencils.  When the pencils are divided between four of her friends, there is one pencil left over.  If they are divided between five friends there are two left over.  Between seven friends there would be four left over.  What is the smallest number of coloured pencils that Alison could have? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem->Step-by-step Calculation