# A 1999 IMO Chinese Team Selection Question

Algebra Level 5

For non-negative real numbers $$x_{1},\: x_{2},\: ...,\: x_{n}$$, which satisfy $$x_{1}+x_{2}+...+x_{n}=1$$, find the largest possible value of $$\displaystyle \sum_{j=1}^{n}(x_{j}^{4}-x_{j}^{5})$$.