Two eggs any style -- generalizing egg-drop experiments

TL;DR

This paper generalizes the classic egg-drop problem to three types, analyzing their structure as binary decision problems and introducing a new efficient algorithm class to optimize the maximum building height tested with limited egg drops.

Contribution

It extends the egg-drop experiment framework to additional types and introduces a non-redundant algorithm class for efficient problem solving.

Findings

All three egg-drop types are binary decision problems.

The paper provides formulas for maximum building height with given egg drops.

A new efficient algorithm class is introduced for solving these problems.

Abstract

The egg-drop experiment introduced by Konhauser, Velleman, and Wagon, later generalized by Boardman, is further generalized to two additional types. The three separate types of egg-drop experiment under consideration are examined in the context of binary decision trees. It is shown that all three types of egg-drop experiment are binary decision problems that can be solved efficiently using a non-redundant algorithm -- a class of algorithms introduced here. The preceding theoretical results are applied to the three types of egg-drop experiment to compute, for each, the maximum height of a building that can be dealt with using a given number of egg-droppings.