$[20$ pts$]$ Sweet Confections, TA Connections

This year for Valentine's Day, the $n2$ CIS$1600$ TAs have decided to exchange candy. Any

TA can exchange candy with any number of other TAs $($including zero$),$ but $2$ TAs can only

exchange candy once. Prove or disprove that there must always be $2$ TAs who exchanged candy

with the same number of people.