A single process cannot form a circular resource dependency here.
Now check whether two processes can deadlock.
$P_1$ and $P_2$ have only $R_2$ in common.
$P_1$ does not require $R_3$, and $P_2$ does not require $R_1$.
So they cannot hold different resources required by each other to form a two-process cycle.
Similarly:
- $P_1$ and $P_3$ share only $R_1$.
- $P_2$ and $P_3$ share only $R_3$.
No pair can construct a circular wait.
$P_4$ requires only $R_2$. If it obtains $R_2$, it has no second resource to wait for. If it waits for $R_2$, it does not contribute another held resource to a cycle.
But three processes can deadlock:
- $P_1$ holds $R_1$ and waits for $R_2$.
- $P_2$ holds $R_2$ and waits for $R_3$.
- $P_3$ holds $R_3$ and waits for $R_1$.
This produces:
$P_1\rightarrow P_2\rightarrow P_3\rightarrow P_1$.
Therefore the minimum number is $\boxed{3}$
