I was recently chatting with Dr. David Nacin, a fellow puzzle enthusiast who has taken a keen interest in solving, studying, and sharing my Haunted Mirror Maze puzzles. For the uninitiated, Haunted Mirror Maze puzzles present a top-down view of a hall of mirrors. The mirrors are aligned to a grid, and empty spaces must be filled with some number of vampires, ghosts, and zombies. However, Dr. Nacin relayed a query he received in the course of sharing the puzzles:
An interesting idea. Someone asked if the mirror squares were always given in the monster maze puzzles.
I wonder if it’s still possible to get a unique solution even in small cases with only knowing the number of mirrors and their direction.
Interesting idea could be figuring out when the mirrors don’t have to be given.
Our discussion turned to the types of clues that would allow for satisfying break-ins for the puzzles: singular 0 clues that indicate no path would be monster-less, or perhaps some ‘superlative’ clues where the line of sight contains nearly every monster.
Given this set of constraints, we both tried creating some small sample puzzles. One point which we had not agreed on was whether to enumerate the direction of the mirrors. It was interesting to see how the added constraint of specifying mirror direction could lead to uniquely solvable puzzles that would not be uniquely solvable otherwise.
With David’s permission, I’m happy to share some of our sample puzzles from our ‘puzzle jam session’ below.