In order to maintain functionality, a cluster must have what minimum number of nodes if it can't lose 3 or more nodes?

To determine the minimum number of nodes required for a cluster to maintain its functionality without losing 3 or more nodes, the correct answer is rooted in the concept of redundancy and fault tolerance within clustered systems.

When a cluster cannot afford to lose 3 nodes, it’s essential to ensure that there is still a majority of nodes available to make decisions and process requests. In general, a cluster operates effectively as long as a majority of its nodes are functioning properly. The formula used to calculate the minimum number of nodes needed in a system capable of withstanding failures involves the requirement to have more than half of the total nodes operational.

The provided choice, which states that a cluster must consist of (# of nodes / 2) + 1, aligns precisely with this principle. This formula ensures that, even in the event of losing a certain number of nodes (in this case, up to 3), a majority will still remain, thus maintaining the cluster's functionality.

For example, if you have a cluster of 6 nodes, losing up to 3 means you could end up with only 3 nodes remaining. To maintain functionality, you need at least 4 nodes (which is more than half of 6). Applying the formula (# of nodes