Holiday Contest 2025 - Individual Round - Problem 1

Max is helping Santa sort stockings for 100 different families. Each family has one unique pair of stockings (the two stockings in a pair of stockings are different), and Max draws stockings one by one, randomly and without replacement, from Santa's stocking bag. What is the minimum number of stockings Max must draw to guarantee he has a pair of stockings for 30 distinct families?