Question 102
Is it possible to partition a set $M$ of positive integers into some disjoint subsets so that in each subset one of the numbers is equal to the sum of all other numbers of this subset if
$$
\text{a) } M = \{1, 2, \dots, 20\} \text{?}
$$
$$
\text{a) } M = \{1, 2, \dots, 20\} \text{?}
$$