There are several stones, the mass of each of which does not exceed 2 kg, and the total mass is 100 kg. From them, several stones are selected, the total mass of which differs from 10 kg by the smallest possible number $d$ for this set. What is the maximum value that the number $d$ can take for all possible sets of stones?
Example. For a set of 55 stones weighing ${ }^{20} / 11$ kg, the number $d$ is ${ }^{10} / 11$ (you need to take 5 or 6 stones).

Suppose that for some set of stones weighing $x_{1} \geq x_{2} \geq \ldots \geq x_{n}$, the number $d$ is greater than ${ }^{10} / 11$. Choose $k$ such that $x_{1}+\ldots+x_{k-1} \leq 10 \leq x_{1}+\ldots+x_{k}$. According to the assumption, $x_{1}+\ldots+x_{k-1}10+$ $10 / 11$. Therefore, $x_{k}>20 / 11$. By the condition $x_{i} \leq 2$, so $k>5$, that is, $k-1 \geq 5$. Thus, $x_{1}+\ldots+x_{5} \leq x_{1}+\ldots+x_{k-1}5 \cdot{ }^{10} / 11$. Therefore, the weight of the set of the first five stones differs from 10 kg by less than $10-100 / 11=10 / 11$ kg. Contradiction.

## Answer

$10 / 11$