To determine the value of $y$ in Figure (III), let's analyze the pattern observed in Figures (I) and (II).

1. Observing the Pattern:

   • In Figure (I), the four numbers are $2$, $5$, $1000$, and $1$.
   • In Figure (II), the four numbers are $9$, $10$, $100$, and $45$.
   • In Figure (III), the known numbers are $5$, $10$, $1600$, and $y$.

   By comparing these figures, we notice that each figure might have a pattern involving multiplication, division, or addition/subtraction to generate the missing value.

2. Finding the Relation:

   • In Figure (I), let's analyze if there’s a multiplicative or additive relation between the numbers: $2 \times 5 = 10 \quad \text{and} \quad 1000 \times 1 = 1000$
   • In Figure (II), checking similar combinations: $9 \times 10 = 90 \quad \text{and} \quad 100 \div 45 = \text{(No simple pattern found here)}$

After exploring these approaches without a clear multiplicative or additive relationship, the values do not immediately indicate a recognizable arithmetic or geometric progression.

Let me know if you want further analysis or pattern-checking steps for this problem.