Question 150
10,000 kids came to a camp; each has exactly 11 friends at the camp (friendship is always mutual). Each kid wears a T-shirt of one of the seven fixed colors, so that every two friends wear T-shirts of distinct colors. The guides requested that some kids (at least one) change their T-shirt colors (with some others among the same seven colors). A short poll showed that there are 100 kids which reject changing colors of their T-shirts. Prove that some remaining kids still can change their T-shirt colors so that the condition that every two friends wear distinct colors persists. (A. Magazinov)