Logic Masters Deutschland e.V.

FREXIT ! by Patrick JUNKE

Administrative rules of the EU grid :

Art. 1.1 : All columns contain each digit from 1 to 9.
Art. 1.2 : All rows contain each digit from 1 to 9.

Art. 2.1 : All NOT-PRIME digits (1,4,6,8,9) form a labyrinth⁽¹⁾.
Art. 2.2 : All ODD digits (1,3,5,7,9) form a second independant labyrinth⁽¹⁾.
Art. 2.3 : All NOT-DIVISIBLE-BY-3 (1,2,4,5,7,8) digits form a third independant labyrinth⁽¹⁾.

Art. 3.1 : Corridors of the NOT-PRIME labyrinth are always one cell wide⁽²⁾.
Art. 3.2 : Corridors of the ODD labyrinth are always one cell wide⁽²⁾.

⁽¹⁾ i.e. : a single area of orthogonally connected cells. The other cells are to be considered as walls.
⁽²⁾ i.e. : there are no squares of 2 x 2 labyrinth cells.

The stolen map tatooed on the back of François :

"The arrows of the map indicate all the dead ends of the three labyrinths. They point toward the exit of the dead end, you know, toward the only orthogonally cell to which there are connected.

Each indicated dead end cell is a dead end in only one of the three labyrinths.

I know and have marked with dotted squares all the dead ends of the NOT-DIVISIBLE-BY-3 labyrinth.

I can't tell for the other arrows to which labyrinth, ODD or NOT-PRIME, they belong. All I know, if it helps, is that the exit can be reached by the NOT-PRIME labyrinth."

The escape

The NOT-DIVISIBLE-BY-3 labyrinth is not accessible for the people. This part concerns only the NOT-PRIME and the ODD labyrinths.

French citizens start in the cell with the flag. The exit is labelled with the dove.
Cells with the digit 9 are one way vents, so that stepping on a 9 automatically transfers you from one labyrinth to the other, without possible going back with the same vent.
The path taken by the French includes the departure cell. The sum of all the digits of the cells constituting the shortest escape path to the exit is 69. (Count a cell each time you step on it. A digit 9 labyrinth tranfer counts as one step, not two.)

Here is a link to the puzzle on sudokupad.

Important advice : Use the corner pencil marks to keep track of the different paths and walls. It will allow you to select them all with the corner pencil marks button selected, and to attribute them a path or wall color. Keep the central pencil mark for the rest, even found digits, to keep corner marks selectable.

Typically : 1 for path, 2 for walls in ODD labyrinth, 3 for path, 4 for walls in NON-PRIMARY labyrinth, 5 for path, 6 for walls in NOT-DIVISIBLE-BY-3 labytinh. Then for example, if you want to see ODD labyrinth, attribute to all twos a dark color and all ones a light one.

Note : This correspondance table shows you quickly how digits correspond to path cells or wall cells depending of which labyrinth you consider :

Note : Be well aware that this puzzle is filled by negative constrains. Let's recall them : you can't create any unreferrenced dead end, you can't create 2x2 labyrinth square in the ODD and NON-PRIME labyrinths, once a dead end is attributed to one labyrinth, it is not a dead end in the other labyrinths.