I read a while ago about the famous Soviet N-1, called by some the most powerful rocket (in terms of thrust at liftoff) in history. It used an incredible 30 engines in its first stage. The American Saturn V, on the other hand, used only five F-1 engines in its first stage. The difference was that each F-1 was much more powerful than a single one of the (initially NK-15) engines used on the N-1. The advantage of the 30-engine system was that if one engine failed, there were backups, and more fuel could be shifted to or from others to compensate (although this led to some amusing mishaps with the KORD computer controlling the engines).
What are the other advantages/disadvantages for each of the systems (30-engines vs. 5-engines)? What made the Soviets choose a 30-engine system, while the Americans chose a 5-engine system?