binary principle and elephant puzzle

How is a puzzle like the elephant puzzle used to scaffold? (in education, but you can do it among friends too) Well, for one the trick is that you don't need to know how to solve every independent puzzle (exceptions disregarded) to know how to solve a puzzle. For some puzzles, understanding laws is necessary or useful. How switches can be written down as either on or off may be helpful for solving a binary puzzle. Also, the idea of how to list numbers may be important. 00001 comes before 00010 and after 00000.
In the list 00, 01, 10, 11, 100, 101, 110, 111 notice that the last digit changes every time from 0 to 1, before the left digit can change. This also is the case with the elephant puzzle.
This is how a puzzle gives deep insight of maths and logic. Deep because it is a direct experience. It makes a connection between a concept in your head and a visual tactile experience in your hands.