The number $$95$$~\uline{~~~~~~~~~~}~$$94775998$$ is divisible by $$198$$. What is the missing digit? 
Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Already divisible by $$2$$, so we must check it divides by $$9$$ by adding the digits together:  $$9+5+x+9+4+7+7+5+9+9+8=54+x$$, this must be a multiple of $$9$$ so $$x$$ is $$0$$ or $$9$$.  It should also be divisible by $$11$$, so the alternating sum of digits should too.  $$9-5+x-9+4-7+7-5+9-9+8=2+x$$ is divisible by $$11$$.  Hence $$x$$ is $$9$$. 