Question 179
Let us consider the set $A=\{1,2,3,4, \ldots, n\}$. A subset of $A$ is called hierarchical if it satisfies the following two properties: - The subset must have more than one number. - There is a number in the subset that coincides with the sum of the other numbers in the subset. You want to divide the set $A$ into hierarchical subsets.
a) For $n=13$, show that the division cannot be done.
b) For $n=12$, show that such division is possible.
a) For $n=13$, show that the division cannot be done.
b) For $n=12$, show that such division is possible.