Question 1
In a school there are 40 different clubs, each of them contains exactly 30 children. For every $i$ from $1$ to $30$ define $n_{i}$ as a number of children who attend exactly $i$ clubs. Prove that it is possible to organize 40 new clubs with 30 children in each of them such that the analogical numbers $n_{1}, n_{2}, \ldots, n_{30}$ will be the same for them.