In any Base-x system, one digit goes up to x - 1 (with base > 10 we use alphabet letters), then the next digit (to the left) is incremented.
So in our normal Base-10 system, you count up from 0 to 9 and then add a digit in the front and reset the other digits to get 10.

This means, that in every Base-x system ‘10’ equals x.
So you can make the “There 10 types of people …” with every base as ‘10’ in Base-2 means 2, 3 in Base-3 and so on.