Logic Masters Deutschland e.V.

The puzzle was created during my attempt to solve "Kropkiwürfel 3" with minimum head twists.

The board is the surface of a 4x4x4 Acheron cube with some mining tunnels passing through the cube.

There are 16 numbers (1-9 and a-g, where a=10, ..., g = 16) to be placed on the surface of the cube so the numbers on each of the 12 LOOPS and 6 FACES may not repeat.

RULES

- WHITE DOTS are put between each neighbour cells with consecutive numbers. All white dots are given.

- BLACK DOTS are put between each neighbour cells with ratio that is a PRIME NUMBER. The numbers on the black dots indicate the ratio between numbers when the ratio is more than 2. All black dots are given.

- GREY CIRCLES are TUNNEL entrances. Tunnels are ORTHOGONAL to their starting faces and connect cells with ratio that is a PRIME NUMBER (Example: connecting opposite cells 3/9, 1/b, 8/g, etc.). Different tunnels may CROSS underground. All tunnels are given.

Solve online (Penpa+):

Minimal Grid (hard), Default Grid (this), and Helper Grid (ugly, useful)

Good luck and have fun :-)