Two Eggs, 100 Floors

Level 6●●●●○ Hard~8 min

Problem

A building has 100100 floors. There is a threshold floor TT such that an egg dropped from floor TT or above breaks, and from below TT it survives. You have 22 identical eggs. A broken egg can't be reused. Find a dropping strategy that minimizes the number of drops in the **worst case**, and state that worst-case number.