# An algebra problem by Rohan K

Algebra Level 5

Let $$x_1, x_2, \ldots , x_{100}$$ be non-negative real numbers such that $$x_i + x_{i+1} + x_{i+2} \leq 1$$ for all $$i = 1,2,\ldots,100$$, where $$x_{101} = x_1$$ and $$x_{102} = x_2$$.

Find the maximal possible value for the sum $$\displaystyle S = \sum_{i=1}^{100} x_i x_{i+2}$$.

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