Great title, right? Don't worry, I'll explain it.
Here is the story.
The inhabitants of planet Nuri have captured their arch-enemy, the hyperking of a neighboring planet (thus "alien").
They plan to confine him in a labyrinth built out of stone blocks placed on a square grid. They want to take advantage of the curious particularity of how the hyperking can and cannot move. The idea is to prevent him to escape while allowing the Nurians free access to him.
A hyperking moves like a king in chess, except that he moves twice as far (thus "hyper-"). He moves exactly 2 cells in either of the 8 directions. He cannot do otherwise. The spooky thing is that he can do so unhindered by walls, he can tunnel thru solid stone (thus "quantum-tunnelling"). Only the destination cell must be empty.
Unfortunately, Nurian architecture and building technology mandates the following constraints. (Nurikabe-like).
- No 4 blocks in a 2x2 square can all be occupied by rocks. The ground would collapse.
- No 4 blocks in a 2x2 square can all be empty. The ceiling would collapse.
- A solid wall must run around the labyrinth.
- All stone blocks must be connected orthogonally.
- All free cells must form a single orthogonally connected space.
There is a staircase leading down into the labyrinth at each of the 4 corners. The hyperking prison cell connects to the upper left corner. The labyrinth must be designed to prevent the hyperking to move to any other corner of the labyrinth.
Below is a floor plan which fails to prevent the hyperking from escaping. As a warm-up, can you find the path the hyperking can take from the upper left corner to reach another corner?
Your mission now is to fix the labyrinth. Adjust the labyrinth or design a completely new labyrinth on a 19x19 grid, that respects the architectural constraints and prevents the hyperking to travel from his corner to any other corner.
If necessary, you can choose a different size for your labyrinth as long as you have 4 distinct corners inside of the outer wall.
If you think it is impossible, explain why it is so.
- Yes, the hyperking's movement restrictions imply that he can move only to even rows and columns. Or odd rows and columns if you count rows and columns from zero.
- No, the hyperking cannot hyperjump outside of the outer wall. The labyrinth will be built underground, there is compact dirt all around.
- Yes the Nurians could move the exit staircases just one block in either direction to put it out of reach from the hyperking, but no Nurian would accept to build such a horror. Staricases belong to the corners. They have always been there and always will be.
- This is my own creation. The characters and events described in this puzzle are entirely fictious. Any similarity to actual people or incidents is entirely coincidental. No hyperking was harmed in the making of this puzzle.