"You've got N point-equivalent bugs walking on a L cm long stick at 1 cm/s,

starting from N separate points. Each bug falls off when it reaches the edge

of the stick. When two bugs meet in a point, they swap direction and go on

at the same speed.

(a) How many seconds will pass, at most, before all bugs fall out?

(b) How many direction swaps will a bug do, at most?"

Now, I don't want the solution to this problem - I've actually found it.

My question is, can you suggest me some specific text book, or a math topic

to explore, to get better at this kind of problems?

Thanks in advance.