Hi ajazwani1,
You are correct. Three is the minimum number of controllers supported for the APIC cluster due to high availability reasons. For instance, every piece of data in the object model is replicated across the controllers in the cluster, because the cluster acts as a distributed storage and data processing system. Not only does the cluster provide physical redundancy if one APIC goes offline, it also provides database redundancy as well (preventing database corruption).
Why three controllers? Briefly, APICs take advantage of majority and minority concepts. During split brain scenarios (data or availability inconsistencies), an odd number of APICs can allow for a majority (2 APICs communicating), and a minority (an APIC which has lost communication). In this scenario configuration changes can still be made on the APICs part of the majority, while they cannot be made on the APIC in the minority. Whereas, if we started with an even number of APICs it would be very difficult to determine which APIC is part of the majority and which is part of the minority.
For your reference, here's a link to the ACI Troubleshooting Guide which discusses this in detail:
http://aci-troubleshooting-book.readthedocs.org/en/latest/apic.html?highlight=cluster#overview
Hope this helps.
