Two eggs any style -- generalizing egg-drop experiments
This is an incremental theoretical contribution to recreational mathematics and decision tree theory.
The paper generalizes the egg-drop experiment to three types, models them as binary decision problems, and introduces a non-redundant algorithm to compute the maximum building height for a given number of egg-droppings.
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.