A system contains three programs and each requires three tape units for its operation. The minimum number of tape units which the system must have such that deadlocks never arise is ________.

To prevent deadlock among $n$ processes where each process requires a maximum of $m$ resources, the condition for guaranteed deadlock-free operation is:

Here:

• Number of processes ($n$) = $3$

• Maximum demand per process ($m$) = $3$

In the worst-case allocation without causing a deadlock, each process holds $(m - 1) = 3 - 1 = 2$ tape units.

Adding $1$ more resource ensures that at least one process can satisfy its maximum demand, complete execution, and release its resources:

Thus, the minimum number of tape units required is 7.