This question is meant to be solved with pigeonhole principle. But I can't solve it. I just can't figure out what is the pigeon and what is the pigeon hole. I don't really have a clear direction.
Definition: if $X$ is a set of non-negative integers, $\sum X$ is defined to be the summary of all the elements of $X$, for example: if $X =\{2,7,13,20\}$ then $\sum X = 2+7+13+20=42$
Question: let $C \subset \{0,1,2,...,102\}$, $|C| = 10$ ($C$ has 10 elements).
Show that there are sets $A,B \subset C$, such that $A \neq B \neq \emptyset$ and $\sum A = \sum B$
Hint: how many subsets of $C$ are there? What is the maximum for $\sum C$?