Questions such as:
You are walking by a row of $K$ ($4 \le K \le 25$) lights, some of which are on and some of which are off. In this initial conﬁguration, there is no consecutive sequence of four lights that are on. Whenever four or more consecutive lights are on, the lights in that consecutive block will turn off. You can only turn on lights that are off. What is the minimum number of lights you need to turn on in order to end up with all $K$ lights off?
What branch does this fall under? What would be a good book to get started with?