In the Undead Game, what makes one board more difficult than another?
The game is defined like this:
- A 4x4 (or 5x5, etc) grid has some random squares filled with diagonal lines representing mirrors.
- The grid has numbers added on both ends of the rows and the columns, indicating how many undead you will see if you look straight (horizontally/vertically) into the grid from that point.
- You are provided with a set number of zombies, ghosts, and vampires, with the following properties:
- Zombies can always be seen when they are in your line of sight (which extends along the reflection-paths of the mirrors
- Vampires can only be seen if they are directly in your line of sight, but cannot be seen through a mirror
- Ghosts cannot be seen when they are directly in your line of sight, and can only be seen via a mirror.
- Your task is to place the given undead into the empty squares of the grid so that every number around the outside accurately describes the number of undead seen from that point.
An image to help with visualization:
I want to understand what decides the level of difficulty in this game, aside from grid size. For example, the linked website offers 4x4 Easy, 4x4 Normal, and 4x4 Tricky options.
I have written some code to generate a game board and I can generate thousands of 4x4 games by selecting random values for each cell. How do I assign a difficulty to them ?
Is there a way I can do it by just looking at the board ?