Janice needs to buy oranges for several elderly. If she gave $20$ oranges to each elderly, $10$ elderly will not receive any oranges. If she gave $16$ oranges to each elderly, she would have enough oranges to pack $25$ boxes of oranges, each containing $2$ dozen oranges.  How many oranges should Janice give to each elderly so that she gives out all her oranges and that each elderly receives the same number of oranges? 
Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle