$50$ balloons are distributed to Ariel and seven other children. Each of them can get at least one balloon, and no two of them get the same number of balloons. For Ariel, what is the largest possible number of balloons she can get? 
Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value
The largest number of balloons Ariel can get is: $$50 -- (1 + 2 + 3 + 4 + 5+6+7) = 22$$, that is, $$22$$ balloons at most. 