What is the equation for the ZooKeeper ensemble size required to tolerate n faults?

What is the equation for the ZooKeeper ensemble size required to tolerate n faults?

• A. 3n
• B. n+1
• C. 2n
• D. 2n+1

Answer: (D)

To tolerate n faults, you need a quorum that is larger than half the ensemble, so the system can still agree even if n nodes fail. The smallest ensemble that guarantees a majority after any n failures is two times n plus one. With 2n+1 nodes, if up to n fail, at least n+1 nodes remain, which is a majority and can drive leader election and commits. This is why the standard rule is 2n+1: it provides the necessary fault tolerance with the minimal size. For example, 3 nodes tolerate 1 fault, and 5 nodes tolerate 2 faults. The other sizes don’t meet the majority requirement after n faults.

To tolerate n faults, you need a quorum that is larger than half the ensemble, so the system can still agree even if n nodes fail. The smallest ensemble that guarantees a majority after any n failures is two times n plus one. With 2n+1 nodes, if up to n fail, at least n+1 nodes remain, which is a majority and can drive leader election and commits. This is why the standard rule is 2n+1: it provides the necessary fault tolerance with the minimal size. For example, 3 nodes tolerate 1 fault, and 5 nodes tolerate 2 faults. The other sizes don’t meet the majority requirement after n faults.