MathDB

Suppose that the real numbers

a_1, a_2, \ldots, a_{100}

satisfy \begin{eqnarray*} 0 \leq a_{100} \leq a_{99} \leq \cdots \leq a_2 &\leq& a_1 , \\ a_1+a_2 & \leq & 100 \\ a_3+a_4+\cdots+a_{100} &\leq & 100. \end{eqnarray*} Determine the maximum possible value of

a_1^2 + a_2^2 + \cdots + a_{100}^2

, and find all possible sequences

a_1, a_2, \ldots , a_{100}

which achieve this maximum.

Problem Statement