Question 96
A set of numbers is called trilegal if it can be partitioned into three-element subsets in which one element is the sum of the other two. For example, $\{1,2,3,\ldots,11,12\}$ is trilegal because it can be partitioned into $\{1,5,6\}$, $\{2,9,11\}$, $\{3,7,10\}$ and $\{4,8,12\}$.
a. Show that $\{1,2,\ldots,14,15\}$ is trilegal.
b. Show that $\{1,2,\ldots,2010\}$ is not trilegal.
a. Show that $\{1,2,\ldots,14,15\}$ is trilegal.
b. Show that $\{1,2,\ldots,2010\}$ is not trilegal.