## Wednesday, January 13, 2010

### The Egg Drop

A Phoenix Egg is best served hot.

From Neel Tiruviluamala, via Tommy Dickie:

You've been assigned to determine how much force it takes to break a Phoenix egg and you are permitted the use of a 100-story building.  Phoenix eggs are hard and may break if dropped from the first floor or may not even break if dropped from 100th floor.  You need to find the highest floor from which the eggs will not break.  Phoenix eggs are very rare - you only have 2 identical eggs to work with.  Of course you could simply start by dropping an egg from the first floor, then the second floor, and so on until it breaks, but who has time for that?  In the worst-case scenario, in which the egg does not break even from the 100th floor, this would require 100 drops.

What strategy could you employ that requires the fewest number of drops?  Obviously the number of drops required depends on where the egg will break, so you will be judged according to the worst-case scenario.  That is to say, you will be judged according to the maximum number of drops your strategy requires.  Feel free to submit solutions to charlesdguthrie@gmail.com.

On Sunday, if I remember, I will provide a hint.

Hint: There will be 14 drops.  Solution below

Solution:
Drop from the following floors, in order, until the first egg breaks: 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99.  Once the first egg breaks, drop the second egg from the last place the first one DIDN'T break.  For example, if the first egg breaks on floor 39, drop the second egg from floor 28.  Then continue dropping the second egg from floor 30, 31, 32, etc. until it breaks.  No matter what the outcome, you will not have more than 14 drops.  Note: if the first egg doesn't break even at floor 99, save it and the other one because you can assume they will break at floor 100.