2 Eggs and 100 Floors (puzzle)

With two eggs, use decreasing jumps so a break leaves at most as many linear checks as prior jumps: drop at 14, then 27, 39, and so on. The worst case is 14 drops because 14+13+...+1 = 105, which covers 100 floors. If an egg breaks, linearly check from the previous safe floor with the other egg; if not, reduce the next jump. This minimizes the maximum number of drops. Equal-size jumps such as ten lead to a worse worst case of 19. In an interview, make the invariant explicit before writing code, trace a boundary example that breaks a tempting shortcut, state what each stored value represents, and explain why every update preserves correctness. This verification step also surfaces empty-input, duplicate-value, and numeric-limit cases.

Complexity: With two eggs and F floors, the decreasing-step strategy uses O(sqrt(F)) drops in the worst case and O(1) extra space.