$\left[\begin{array}{l}\text { [ Examples and counterexamples. Constructions ]} \\ \text { [ Numerical inequalities. Comparing numbers. ] }\end{array}\right.$

The sum of several numbers is 1. Can the sum of their squares be less than 0.1?
The condition of the problem is satisfied by eleven numbers equal to $1 / 11$. The sum of their squares is $11 \cdot (1 / 11)^2 = 1 / 11 < 0.1$.

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