Sixteen lists some symbols that represent sixteen. All items in the following line stand for sixteen.

10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, __?

What "10" means (whether it is the way we write numbers or some other approach) is just that all single-symbols are gone: we have to start over. If we understand these signs to be the places inside an egg carton they would be single-symbols like:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, and b; or 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b and c

Starting with zero is the way we normally write numbers. So "10" could mean "one dozen".

So if "10" stands for "sixteen" when our "box" begins with a slot labeled zero or "0" and ends after counting out "fifteen" more places, going on to the next number "11" involves a change. The answer to "what kind of change" is the size of the box or number of single-symbols we can use in writing quantities.
In other words the change is in box size - from "sixteen" to "fifteen". We have one more than "fifteen" in a set up where there are only fifteen single symbols or distinct numbers, namely (using single letters for what we ordinarily write as 10, 11, 12, 13 and 14):

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, and e

If we keep changing the size of the box understanding all the numbers 10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24 to represent "sixteen", its size at "13" in the list is "thirteen". At "16" the size goes to "ten". At "22" there are "seven" single-symbols available - 2*7+2 is "sixteen".

Continuing to "__" the box is "five" so we need 3 in the leftmost place, one more in the rightmost, and the missing value "31" is the last representation for "sixteen" in this Example 5 list.