Explanation:

To understand why the largest value of N that will always avoid deadlock is 1, we need to understand the concept of deadlock and how it can occur in a system with limited resources.

Deadlock:
Deadlock is a situation in which two or more processes are unable to proceed because each is waiting for the other to release a resource. In other words, deadlock occurs when there is a circular dependency of resources among processes, resulting in a state where no process can proceed.

Resource Allocation:
In a system with limited resources, it is important to allocate resources effectively to avoid deadlock. Each process can request a maximum of N instances of a resource. In this case, we have 3 resources and 5 processes competing for them.

Resource Allocation Graph:
To analyze the resource allocation and possibility of deadlock, we can create a resource allocation graph. In this graph, each process is represented by a node, and each resource is represented by a resource instance. If a process requests a resource instance, there is an edge from the process node to the resource instance node.

Possible Scenarios:
Let's analyze different values of N and their impact on deadlock:

1. N = 1:
- In this case, each process can request only 1 instance of a resource.
- If a process requests a resource, it can be allocated if available, otherwise, it will wait until the resource is released.
- Since there are 3 resources and 5 processes, it is possible for all processes to acquire at least 1 resource and continue execution.
- This ensures that no circular dependency of resources occurs, avoiding deadlock.

2. N > 1:
- If N is greater than 1, a process can request multiple instances of a resource.
- Suppose N = 2, and all 5 processes request 2 instances of a resource simultaneously.
- In this case, deadlock can occur if each process holds 2 instances and waits for the remaining 1 instance to be released by other processes.
- This creates a circular dependency, resulting in a deadlock state.

Conclusion:
The largest value of N that will always avoid deadlock is 1. By limiting the maximum instances a process can request to 1, we ensure that each process can acquire at least 1 resource and continue execution, avoiding the possibility of a circular dependency and deadlock.

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