I am thinking of a number.  When my number is divided by $3$. it gives remainder $2$.  When my number is divided by $5$, it gives remainder $3$.  When my number is divided by $7$, it gives remainder $4$.  What is the smallest possible value of my number? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem->Chinese Remainder Theorem with Constant Remainder