Difficult puzzle, scaffolding & automatisation

Difficult puzzles need a strategy to be able to solve them. Smart children just try solving them, trusting their solving skills rather than a strategy. This works until they face a puzzle that seems not to work in that way. Then they have to try something called multilayered strategy. This is exactly the aim of scaffolding, getting insight in structure of solution, rather than being able to just solve the puzzle without having to worry how they did it.
In the midst of this comes emotions that are new to smart children: failure, frustration, stress... These emotions are often successfully avoided because smart children often can solve problems easily. When the puzzle is difficult enough, they get the chance to experience these emotions. A good teacher knows that emotions are a part of education. It is good to reflect on the emotions. What happened? How did you feel?
Then the child has to finish the task anyway. This means perseverance. The more perseverance, the better the child will feel when it does succeed to solve the problem in the end.
When they succeeded to solve the difficult puzzle, accompanied with the necessary frustration, the next step is to teach the child to automatize the puzzle.

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.