Find the number that comes in place of the question mark.
$$1:1::?:169$$

Let's analyze the mathematical pattern behind the given analogy ratio:
The first pair is $1:1$, which can be expressed in the form of $x:x^2$ because $1:1^2=1:1$.

Applying the exact same $x:x^2$ logic to the second pair:

$$\text{Given term}=169$$

We know that $169$ is a perfect square:

$$169=13^2=13\times 13$$

Comparing it with $x^2$, we find $x=13$. Therefore, the missing number in place of the question mark is $13$.