Question 83
Red balls and blue balls are put into $n$ transparent boxes. We must choose 50 boxes such that together they contain at least half of the red balls and at least half of the blue balls. Is such a choice always possible, regardless of the number of balls and of the way they were distributed in the boxes, if:
a) $n=100$;
b) $n=99$ ?
a) $n=100$;
b) $n=99$ ?