Math labyrinth

This is a math game that you can make to your friends once you understand it.

To begin with, prepare 12 cards and arrange them in order in a 4×4 grid as the figure.

Tell your friend that the letters represent the rooms of a maze, the rooms are connected by doors vertically and horizontally, not diagonally.

The rooms in the maze will disappear (you will remove the letters) as your friend makes the journey through the rooms mentally.  

But if you follow the instructions, the room where you are located will never disappear and end up trapped in a single room. 

The instructions are as follows:

1. It is necessary to be mentally placed in the letter corresponding to your month of birth (1 =January, 2 =February, ...  J=November, Q=December). You don't have to tell you what that box is. 
2. It must move mentally horizontally or vertically, going backwards if desired, as many movements as indicated in the letter where it is located. You do not have to indicate or give any clue where it is located.
3. Once you have made the tour you have to say "I have already moved"
4. Then you will withdraw some letters.
5. It is necessary to go back to step 2 and follow the cycle 2,3,4 until there is only one card left.

The game is surprising, since despite not knowing what the starting room is or what route is made, the retired cards are never where it is located.

You can play against your computer on this FCRi page where you will also find the explanations and instructions to understand how the game works and the rules to follow to remove cards and thus be able to play the game to friends. 

(this virtual version is the result of a joint MMACA project with the FCRi Catalan Foundation for Research and Innovation)