# Throwing Eggs from a Building

## 1. 问题描述

1.4.24 Throwing eggs from a building. Suppose that you have an N-story building and plenty of eggs. Suppose also that an egg is broken if it is thrown off floor F or higher, and intact otherwise. First, devise a strategy to determine the value of F such that the number of broken eggs is $$\sim lg N$$ when using $$\sim lg N$$ throws, then find a way to reduce the cost to $$\sim 2lg F$$.

## 2 问题扩展

1.4.25 Throwing two eggs from a building. Consider the previous question, but now suppose you only have two eggs, and your cost model is the number of throws. Devise a strategy to determine F such that the number of throws is at most $$2\sqrt{N}$$, then find a way to reduce the cost to $$\sim c\sqrt{F}$$. This is analogous to a situation where search hits (egg intact) are much cheaper than misses(egg broken).

## 3 更多的鸡蛋～

1. 首先，得确定第一个步长$$x_1$$
2. 如果碎了，则问题转换成了2个鸡蛋$$x_1-1$$层楼的问题，（根据前面的方法假设该问题的最优解为$$x_c$$)；
3. 如果没碎，则转换成3个鸡蛋$$N-x_1$$层楼的问题