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The house of Santa Claus is an old German drawing game for small children. You have to draw a house in one line.  You must not lift your pencil while drawing. $\color{red}{\text{You must not repeat a line.}}$

A possible solution for drawing such a house is:

The drawings sequence is here: 1->2->4->1->3->4->5->3->2

How can one find out all existing drawing sequences using Mathematica?

UPDATE:

each starting position should be possible and the last line should end at the starting postion.

The house of Santa Claus is an old German drawing game for small children. You have to draw a house in one line.  You must not lift your pencil while drawing. $\color{red}{\text{You must not repeat a line.}}$

A possible solution for drawing such a house is:

The drawings sequence is here: 1->2->4->1->3->4->5->3->2

How can one find out all existing drawing sequences using Mathematica?

UPDATE:

Each starting position should be possible and the last line should end at the starting position.

The house of Santa Claus is an old German drawing game for small children. You have to draw a house in one line.  You must not lift your pencil while drawing. You must not repeat a line.

A possible solution for drawing such a house is:

The drawings sequence is here: 1->2->4->1->3->4->5->3->2

How can one find out all existing drawing sequences using Mathematica?

UPDATE:

each starting position should be possible and the last line should end at the starting postion.

The house of Santa Claus is an old German drawing game for small children. You have to draw a house in one line.  You must not lift your pencil while drawing. $\color{red}{\text{You must not repeat a line.}}$

A possible solution for drawing such a house is:

The drawings sequence is here: 1->2->4->1->3->4->5->3->2

How can one find out all existing drawing sequences using Mathematica?

UPDATE:

each starting position should be possible and the last line should end at the starting postion.

The house of Santa Claus is an old German drawing game for small children. You have to draw a house in one line.  You must not lift your pencil while drawing. You must not repeat a line.

A possible solution for drawing such a house is:

The drawings sequence is here: 1->2->4->1->3->4->5->3->2

How can one find out all existing drawing sequences using Mathematica?

The house of Santa Claus is an old German drawing game for small children. You have to draw a house in one line.  You must not lift your pencil while drawing. You must not repeat a line.

A possible solution for drawing such a house is:

The drawings sequence is here: 1->2->4->1->3->4->5->3->2

How can one find out all existing drawing sequences using Mathematica?

UPDATE:

each starting position should be possible and the last line should end at the starting postion.