Teacher Nicole bought some badges and divided it equally among $8$ children. If everyone got $9$ badges, there would still be some badges remaining. What is the biggest possible and smallest possible number of badges Teacher Nicole could have bought? 
Overseas Competition->Knowledge Point->Calculation Modules
~\uline{~~~~~~~~~~}~$\div 8=9$ $\text{R}$~\uline{~~~~~~~~~~}~  Biggest possible remainder is $7$ while smallest possible remainder is $1$.  Biggest possible number of badges is $$8\times 9+7=79$$, while the least possible number of sweets is $$8\times 9+1=73$$. 