$\begin{aligned} & \text { [ Examples and counterexamples. Constructions ] } \\ & \text { [Numerical inequalities. Comparing numbers.] }\end{aligned}$

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 $11 \cdot (1 / 11)^2 = 1 / 11 < 0.1$.

## Answer

Yes.