Find a whole number between $$200$$ and $$400$$ that has the following properties.  When the number is divided by $$3$$ the remainder is $$2$$.  When the number is divided by $$4$$ the remainder is $$2$$.  When the number is divided by $$5$$ the remainder is $$2$$.  When the number is divided by $$7$$ the remainder is $$5$$.  What is the number? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems