Question 12
There are $2025$ people and $66$ given colors. Each person has $66$ balls, one of each color, with a total weight of $1$ for all $66$ balls.
Find the smallest real number $C$ such that, no matter how the balls are weighted, one can always select exactly one ball from each person so that for every color, the total weight of the selected balls of that color does not exceed $C$.
Find the smallest real number $C$ such that, no matter how the balls are weighted, one can always select exactly one ball from each person so that for every color, the total weight of the selected balls of that color does not exceed $C$.