There are many red balls, yellow balls, and blue balls of identical shape in a bag. Many students are playing a game in which each of them can take $$2$$ balls from the bag without observing the color of the balls. (After each student takes the balls, they should put them back in the bag.) The teacher finds that no matter how the students take the balls, there are always at least $$2$$ students who take the same balls. (For example, student $$A$$ and student $$B$$ both get one red ball and one yellow ball.) There would be at least~\uline{~~~~~~~~~~}~students playing the game. 
Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
There are $$6$$ possible cases when taking $$2$$ balls from the box. In the worst case, each of the first $$6$$ students takes different balls to the others. When the $${{7}^{\text{th}}}$$ student takes the balls, he/she would definitely take the same balls with someone among the first $$6$$ students. $$6+1=7$$. 