Which of the following numbers leaves a remainder of $$1$$ when divided by $$2$$ and $$3$$? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem
When we divide by $$2$$, $$3$$, the remainder is $$1$$. Hence, if we first subtract $$1$$, the result will be divisible by $$2$$, $$3$$.  $2\times3+1=7$ 