We can start by writing out the information we have:

- The sum of all the digits of q is x13.
- q is a multiple of 10n.

Let's first focus on the second piece of information. If q is a multiple of 10n, that means it has n zeroes at the end. For example, if n=3, then q could be 1000, 2000, 3000, and so on. We don't know exactly what q is, but we do know that it ends in n zeroes.

Now let's look at the first piece of information. The sum of all the digits of q is x13. This means that if we add up all the digits of q, we get a number that ends in 13. For example, if q was 123456789, the sum of its digits would be 1+2+3+4+5+6+7+8+9 = 45, which ends in 13.

So how can we use these two pieces of information to find q? Well, let's think about what the sum of the digits of q can be. The smallest possible sum is 1 (if q is just 1), and the largest possible sum is 9n (if q is a string of n nines, such as 999 if n=3). But we know that the sum of the digits of q ends in 13, so we can narrow down the possibilities.

For example, if n=3, then the sum of the digits of q could be 13, 23, 33, 43, 53, 63, 73, or 83. We can eliminate some of these possibilities based on what q is a multiple of. For example, if the sum of the digits of q is 13, then q could be 10, 100, 1000, etc. But q can't be 10, because that's not a multiple of 1000. So we can eliminate the possibility of the sum of the digits of q being 13.

Continuing in this way, we can narrow down the possibilities for the sum of the digits of q based on what q is a multiple of. Eventually, we'll end up with just one possibility for the sum of the digits of q, and we can use that to find q. For example, if we find that the sum of the digits of q must be 83, then we can start trying out multiples of 1000 that add up to 83: 2999, 3998, 4997, etc. We can check each one to see if it works, and eventually we'll find the right q (in this case, it's 4997).